What is called a decimal fraction. Decimal fractions: decimal, record, butt, diz with decimal fractions. Subdivided the decimal fraction and integer number on the whole number that per decimal fraction

Decimal fractions are subdivided into three advanced classes: final tens fractions, non-stop periodic tens fractions and non-stop non-periodic tens fractions.

Chinese tens fractions

Appointment. Kіncevim decimal fraction (decimal fraction) call others or change the number that the banner can be 10, 100, 1000, 10000, etc.

For example,

Up to tens of fractions, such fractions are added, as they can be brought up to fractions, which the banner of 10, 100, 1000, 10000 and so on, for the help of the main power of fractions.

For example,

Firmness. A short simple drіb or a non-short zmіshane nesіle number є kіntsevym decimal fraction, even and only just, if the laying out of їz znamennikіv on simple multipliers to avenge like multipliers are more than the number 2 and 5, moreover, in sufficient steps.

For decimal fractions, use special recording method , vikoristovuyuchi to whom. Zliva in Komi is recorded as a number of fractions, and the right-handed is the number of shot fractions, in front of which such a number of zeros are added, so that the number of digits after Komi is equal to the number of zeros in the denominator of the decimal fraction.

For example,

Respectfully, that the tenth drіb does not change, so as to attribute a sprat of zero to the right-hander or the left-hander to the new one.

For example,

3,14 = 3,140 =
= 3,1400 = 003,14 .

Figures to stand in front of the coma (levoruch vіd komi) in tenth record end decimal fraction, approve the number, yak name whole part of a decimal fraction.

The numbers that stand after the Komi (right-handed in the Komi) at the tenth record of the final tenth fraction are called decimal places.

The final decimal fraction has the final number of decimal places. Dozens of signs form fraction fraction.

Multiply and subdivide decimal fractions by 10, 100, 1000 and so on.

In order to multiply the decimal point by 10, 100, 1000, 10000 and so on., enough move someone to the right on 1, 2, 3, 4 too thin. tens signs are clear.

Already at post school learners stick with fractions. And then the stinks come from the skin. It is impossible to forget dії іz by numbers. That is why it is necessary to know all the information about primary and tens fractions. The understanding is clumsy, the smut is sorted out in the usual order.

Need more fractions?

Navkolishnіy svіt is composed of whole objects. I also don’t have much to consume in private. Zate everyday life constantly nashtovhuє people pratsyuvati with parts of subjects and speeches.

For example, chocolate is made up of a lot of small pieces. Let's take a look at the situation, if one tile is covered with twelve squares. If you divide into two, then you will cut into 6 parts. It's good to split up into three. And the axis of five times cannot be given for a whole bunch of chocolate.

Before speech, qi chastochki - already fractions. And further їхнє podіl to produce before the appearance of more collapsible numbers.

What is "drob"?

This is the number that is made up of the parts of one. The ringing looks like two numbers, separated by a horizontal or frail boundary. Tsya rice is called shot. The number written down to the beast (levoruch) is called a numeral. Those who stand below (right-handed), are the standard.

In fact, the shot characteristic is shown by the sign below. So the numeral can be called dilimim, and the signer can be called dilim.

How to use fractions?

Mathematics has only two types: simple and tens of fractions. The first schoolchildren to know the cob classes, calling them simply “fractions”. Others are recognized in class 5. The very same names are called.

Zvichaynі fractions - all those that are written down by looking at two numbers divided by rice. For example, 4/7. Desyatkov - the whole number, in which the fraction of shots can be a positional record and vodokremlyuєtsya as a whole for the aid of the Komi. For example, 4.7. It is necessary for me to learn clearly that two pointed butts are needed for different numbers.

skin simple drіb can be written at the sight of the tenth. Tse firming mayzhe zavzhdi є vіrnim і at the gate directly. Іsnuyut rules, yakі allow you to write down the decimal fraction with a decimal fraction.

How can you see shots?

More often than not in chronological order, shards of stench curl up. The first to go are simple fractions. Among them you can see 5 subdivided.

Correct. Її the numeral keeper is smaller than the banner.

Wrong. She has a larger numeral book or a better one for the bannerman.

Short / slow. She can appear as right, so wrong. It is important іnshe, chi є at the number book with the banner of the spіlnі multipliers. If so, then it is necessary to spread insulting parts of the shot on them, so as to speed up yoga.

Zmishan. To її voicing ї correct ї (wrong) shot part is attributed to the whole number. Moreover, it’s always worth it to be left-handed.

Skladova. It is settled from two divisions one by one shots. That is why there are once three shot rice in it.

Decimal fractions have only two subdivisions:

kіntseva, tobto that, at which the dribna part is obmezhena (maє kіnets);

neskіchenna - a number for which the numbers after komi do not end (їх can be written neskіchenno).

How to translate the tenth drib from the great?

If it is the last number, then the association will be established, based on the rules, as I feel, so I write. Tobto it is necessary to read correctly and write it down, but without Komi, but with shot rice.

Like a hint about the necessary banner, it is necessary to remember that the wine is always alone and the sprat is zero. The rest is necessary to write styles, numbers of numbers in the other part of the examined number.

How to translate tens of fractions from the zvichay, so that the whole number is a fraction of a day, so it is equal to zero? For example, 0.9 or 0.05. After stopping the designated rule, it is necessary to enter zero integers. Ale vin does not show up. It is left to write down only the smallest parts. The first number has the sign of dorivnyuvatime 10, the other has 100. To be appointed, apply the matimut numbers: 9/10, 5/100. Moreover, the rest can be shortened by 5. Therefore, the result for it is necessary to write down 1/20.

How is it from the tenth fraction of the zrobiti zvichayny, how is it that the whole of the whole is part of the vіdmіnna from zero? For example, 5.23 chi 13.00108. In both butts, the whole part is read and the value is written down. The first one has a score of 5, the other one has 13. Then, it is necessary to proceed to the shot part. It is necessary for them to carry out that very operation. The first number has 23/100, the other has 108/100000. Another value will need to be quick again. Vіdpovіdі have such mixed fractions: 5 23/100 and 13 27/25000.

How to translate the inexhaustible dozens of words from the great?

If it is not periodic, then such an operation cannot be carried out. Tsey fact po'yazany z scho, schoen dozens of drіb zavzhdi be translated either into kontsevy or periodic.

The only thing that is allowed to work with such a fraction is to round it up. Aletodі dozens will be approximately the same, as if inexhaustible. Її can already be turned into a sound. But the reverse process: translated to the tenth - by no means give an ear value. Tobto unscrambled non-periodic fractions in the zvichayn is not translated. Tse next to remember.

How to write down an inexhaustible periodical drib at a visually splendid one?

In these numbers, after the Komi, there are always one or a few repeating digits. Їх is called a period. For example, 0.3 (3). There is a "3" for the period. They can be brought to the class of rational ones, shards can be transformed into simple fractions.

Tim, who smelt with periodic fractions, it seems that stinks can be pure chimes. In the first season, the period begins at the same time in Komi. For another, a small part begins with a thousand digits, and then a repetition begins.

The rule that it is necessary to write down as a great fraction the inexhaustible ten, will be different for the significance of two kinds of numbers. It is easy to write pure periodic fractions with remarkable ones. Like from kіtsevimi, you need to remake them: write down the period in the number book, and the number 9 will be the standard, so the styles of times are repeated, the numbers of numbers are to revenge the period.

For example, 0(5). There are no whole parts of the number, so it’s necessary to proceed to the shot. Write down 5 in the number book, and 9 in the banner.

The rule is about those, how to write down the great tenth periodic rub, which we will change.

Look at the dozhina period. Stilki 9 Matima banner.

Write down the banner: a bunch of nines, then zeros.

To designate a number book, it is necessary to write down the difference between two numbers. All the figures change after the Komi, at the same time with the period. Vіdnіmaєtsya — out there without a period.

For example, 0.5(8) - write down the periodic tens of drib at the visually sizable one. The other part before the period has one digit. So zero will be one. The period also has less than one number - 8. That's one nine. Tobto the bannerman required to write 90.

For the appointment of the numeral of 58, it is necessary to enter 5. To go out 53. In the event, for example, I happen to write down 53/90.

How to translate smaller fractions to decimals?

The simplest option is the number, the banner of which has the number 10, 100 and more. Then the banner is simply visible, and a coma is placed between the shot and the whole part.

There are situations when the bannerman is easily transformed into 10, 100 too thin. bud. For example, the numbers 5, 20, 25. x x multiply by 2, 5 and 4 is correct. It is only necessary to multiply like a banner, and the th number by the same number.

To decide on vipadkiv, you need a simple rule: divide the number on the banner. In this way, there can be two variants of vidpovidey: the last one or the periodic tenth one.

Dії zі great fractions

Additional information

Learn to know them earlier for others. Moreover, the same banners may be stacked with fractions, and then we will differ. Global rules you can call up such a plan.

Know the least blatant multiple of the znamenniks.

Write down the additive multipliers to all outstanding fractions.

Multiply the numerals and the banners by the songs for them multipliers.

Fold (remove) the numbers of shots, and remove the blazing banner without changing.

If the numeral of the smaller one is seen, then it is necessary to say, before us the number is changed, or the correct one.

For the first time, the whole part is obliged to take one. Add a banner to the number plate. And then we will vikonuvat vіdnіmannya.

For the other, it is necessary to zastosuvat the rule of vіdnіmannya z smaller number more. So from the module you can see the module of the changed one, and put the “-” sign in the output.

It is respectful to marvel at the result of the addition (review). If you see the wrong thing, then you need to see the whole part. To add a number to the banner.

Plural and rose

For vikonannya, it is not necessary to bring the shot to the standard banner. Tse feel better vikonannya diy. Ale, they all have one trace of rules.

When multiplying great fractions, it is necessary to look at the numbers of numerals and banners. Like a numeral, that banner can be a double multiplier, you can speed it up.

Multiply numbers.

Multiply the signs.

Yakshcho viyshov speedy drіb, then yogo need to ask again.

In case of a split, it is necessary to change the hand, and replace it with a plural, and a dilnik (another one) - with a return (remember the numeral and banner with the help of the moons).

Potim dіyati, like from multiple (starting from point 1).

In tasks, de multiplying (dіliti) the whole number is necessary, the rest is necessary to write down as an incorrect fraction. Tobto with a banner 1. Let's sweat, as described above.



Dії with decimal fractions

Additional information

Zvichaynno, you can always turn a dozen drіb into a sizable one. І d_yati for the already described plan. Ale іnodi zruchnіshe dіyati without translation. The same rules for their folding and vіdnimannya will be absolutely the same.

Give the number of digits in the fractional part of the number, tobto after Komi. Assign a number of zeros to the missing one.

Write down the fractions so that the coma opines under the coma.

Fold (read) like natural numbers.

Tell someone.

Plural and rose

It is important that there is no trace to add zeros. Fractions need to be left in that look, like the stench of given in the butt. And let's follow the plan.

For multiplication, it is necessary to write fractions one under one, without brutal respect for the Komi.

Multiply like natural numbers.

Put at the top of the coma, in the right end of the right end of the right end, put the digits of the numbers, the arrows of their numbers in the shot parts of both multipliers.

For the bottom, it’s necessary to remake the dilnik: work yoga natural number. Tobto multiply yogo by 10, 100 and so on, depending on how many numbers are in the other part of the dilnik.

Multiply the subdivision by those number.

Divide the tenth drib by a natural number.

Put at the vіdpovіdі to whom at that moment, if you finish rozpodіl whole parts.



Like buti, like in one butt, do you see shots?

And in mathematics, there are often used butts, in which it is necessary to create subscripts over the largest and decimal fractions. Such zavdannya can have two ways of cherishing. It is necessary to objectively call the numbers and choose the optimal one.

The First Way: Reveal the Names by Tens

Vіn come, yakshcho when rozpodіlі chi perekladі come out kіntsevі fractions. For example, if you want one number, you give a periodic part, which is blocked by the method of zastosovuvaty. To that, it’s not appropriate to practice with great fractions, it’s possible to praise them.

Another way: write down dozens of fractions

This reception seems to be handy, as if the parts after the Komi were to cover 1-2 digits. If there are more of them, maybe even a great splendid dream and dozens of records will allow you to make the task easier and simpler. Therefore, it is necessary to seriously evaluate the task and choose the simplest method of solving.

In these articles, we will discuss with you, what is the dozens of drіb, if there are special features and power. Let's go! 🙂

Ten drib є okremim vpadkom zvichaynyh drobіv (yakoy znamennik multiple of 10).

Appointment

Decimals are called fractions, the banners of such numbers, which are added up from one and a dozen of the zeros following it. Tobto are fractions from the standard 10, 100, 1000, etc. Otherwise, the tenth drib can be characterized as a drib with a banner 10 or one of the steps of a dozen.

Apply fractions:

, ,

A dozen drіb is recorded differently, lower sig- nificant. Operations with these fractions are also important for operations with significant ones. The rules of diy over them are close to the rules of diy over whole numbers. Tsim, zokrema, wised up on their demand for the fulfillment of practical tasks.

Submission of a fraction in the tenth entry

The record of the tenth fraction has no banner, the new one has the number of the numeral. For the infamous looker, the record of the tenth fraction is written according to the following scheme:

de X - the whole fraction of a fraction, Y - the її fraction of a fraction, "," - a dozen of coma.

For the correct manifestation of the splendid fraction, it is necessary to look at the tenth, so that the wine is correct, so with the seen whole part (as it is possible) and the numeral, which is smaller than the banner. Then in the tenth entry, the whole part is written down to the tenth komi (X), and the number book of the great fraction - after the tenth komi (Y).

If in the numeral book there is a number with a number of signs, smaller, a lower number of zeros in the znamennik, then in part Y there is an insufficient number of signs in the tenth entry, it will be filled with zeros in front of the digits of the numeral book.

Butt:

If the difference is less than 1, that is. there are no whole parts, then X looks like 0 for the tenth.

At the fractional part (Y), after the remaining significant (remaining zero) order, a sufficient number of zeros may be entered. We add to the value of the fraction. First of all: all zeros, for example, the fractional part of the tenth fraction, can be omitted.

Reading tens fractions

Part X is read in vipadku like this: "X whole".

Part Y is read clearly to the number in the banner. For banner 10 next read: Y tenths, for banner 100: Y hundredth, for banner 1000: Y thousandths and so on ... 😉

The correct one is respected by the other pidkhіd before reading, the foundations for the pirakhunka of the number of discharges in the shotgun part. For whom it is necessary to understand that the shot discharges are stashed at the mirror one according to the distance to the discharge of the whole part of the shot.

The name for the correct reading is indicated in the tables:

Vykhodyachi zgogo, reading may spiratis on vіdpovіdnіst naming order of the remaining digits of the shot part.

• 3.5 reads like "three and five ten"
• 0.016 reads like "zero or sixteen thousand"

Converting a large fraction to a decimal

If there are 10 steps in the banner of the splendid shot, or if there are dozens of feet, then the shift of the shot is counted as described above. In other situations, you will need additional transformations.

Use 2 ways to translate.

The first way I will translate

It is necessary to multiply the number of the numeral and the banner on such a number, so that the number 10 or one of the steps of the tens would be taken away from the banner. And then the drib is given in the tenth entry.

This way to zastosovuetsya for shots, the banner of which is laid out only on 2 and 5. So, at the front butt . Well, if there are other simple multipliers (for example,), then you can get to the 2nd method.

Another way to translate

The 2nd method uses the rozpodіlі of the numeral on the banner at the stovpchik or on the calculator. The whole part, as such, does not take part in the converted.

The rule of splitting into stovpchik, which results in up to a decimal fraction, is described below (div. Divided decimal fractions).

Converting the decimal fraction to the greatest

For this next її, the shot part (right-handed in the Komi) is written down at the counter of the number, and the result of reading the shot part is at the counter of the counter. Dali, yakscho it is possible, it is necessary to speed up the withdrawal of drіb.

Kіntseviy i neskіchenny tens drіb

Kіntsevim is called a dozen drib, a fraction of a shot that is added up from the kіlko digits.

Vishche vsі navedіnі butt vengeance itself kіntseї tensії fractions. However, it is not possible to imagine any remarkable drіb in the sight of the end tenth. For example, the 1st way of translating for this fraction does not stop, and the 2nd way demonstrates that it was impossible to complete it, which means that there can be only a few dozens of fractions.

It is impossible to write down the inexhaustible rubbish in a completely different way. For an unfamiliar person, such fractions can be imagined:

1. as a result of shortening to the bagan number of ranks after the Komi;
2. look like a periodic fraction.

Drib is called periodic, in which case of Komi one can see a sequence of numbers, which are repeated incessantly.

Other fractions are called non-periodic. For non-periodic fractions, only the 1st method of submission (rounding) is acceptable.

The butt of a periodic shot: 0.8888888 ... Here the number 8 is repeated, obviously, it is repeated to the point of inconsistency, the shards cannot be allowed to go any further. What number is called period fraction.

Periodic fractions become pure and mixed. We clean the dozens of rubbish, for which period begins without intermission after the Komi. Zm_shany fraction until the period after Komi may 1 or more digits.

54.33333 ... - periodic clean decimal fraction

2.5621212121… – periodical flutter

Apply to the record of innumerable tens fractions:

In the 2nd butt, it is shown how to correctly draw up a period for recording a periodic fraction.

Translation of periodic decimal fractions in zvichayn

To translate a pure periodic fraction into a significant period, write down a number, and write a number into the standard, which adds up to nines in a number, which is more than a number of digits in a period.

The shifting periodical tenth drib is shifted in this order:

1. it is necessary to formulate the number that is added up from the number, which costs after the Komi to the period, that of the first period;
2. in the subtracted number, take into account the number that will cost after Komi until the period. Podsumok warehouse numeral zvichayny fraction;
3. it is necessary to enter in the banner a number that is made up of the number of nines, equal to the number of digits of the period, and after them zero, the number of such more expensive number of digits of the number, which cost after Komi until the 1st period.

Matching tens fractions

Dozens of fractions rank one by one for whole parts. More than that drib, which has a greater part of it.

Even though the numbers of the part are the same, they equalize the numbers of the corresponding rows in the shot part, starting from the first (from the tenth). Here is the same principle: more than that of fractions, which has a greater order of ten; for the equalness of the numbers in a row of ten, they are ranked in a row of hundreds of thinly.

Oskilki

, oskіlki with equal number of parts and equal tenths of the shot part, the 2nd shot has a larger number of cents.

Adding and adding tens fractions

Dozens of fractions are added and read in the same way, like the whole number, having written down the double digits one and one. For whom it is necessary, for one under one there were dozens of Komi. Todi singles (dozens thinly) of the whole part, and to find ten (hundreds thinly.) Shotguns appear clearly. Discharge the shotgun particles, which are to be rejected, filled with zeros. without middle the process of folding and vіdnіmannya zdіysnyuєtsya so itself, like і for tsіlih numbers.

Multiplication of tens fractions

For multiplying tens of fractions, it is necessary to write them down one under one, vibrating behind the rest of the figure and not exalting respect in the place of spreading tens of lumps. Then it is necessary to multiply the numbers in the same way, like when multiplying whole numbers. After subtracting the result of the following, reconsider the number of digits after the Komi in both fractions and add the Komi to the resulting total number of shot discharges. If there are no discharges, the stench is replaced by zeros.

Reproduction and division of decimal fractions by 10 n

Tsі dії simple that zvodatsya until the transfer of the tenth Komi. P when multiplying the coma, move to the right (fractions are increased) by the number of signs, equal to the number of zeros in 10 n, where n is the full number of steps. Tobto kіlka digits are transferred from the shot part to the whole. When rozpodіlі, vіdpovіdno, coma is transferred to the left (the number changes), and deyaka part of the digits is transferred from the whole part to the shot. If there are not enough digits for transferring, then discharge, which are daily, filled with zeros.

Subdivided the decimal fraction and integer number on the whole number that per decimal fraction

Rozdil at the top of the tenth fraction on the whole number is counted similarly to the subdile of two whole numbers. Dodatkovo is needed only the appearance of the position of the tenth Komi: when the numbers are entered in a row, for some next coma, it is necessary to put someone after the current figure of the census, which is being formed. Then it is necessary to continue the extension until it reaches zero. As a sign at the dilemma of the second marriage, the role of the next victorious is zero.

Similarly, 2 whole numbers are added to the column, so that all the numbers of the subdivided are entered, and the next division is completed. In this case, after the loss of the remaining figure of the divisible, put 10. Coma in the case of the change that is being formed, and as the figure of the loss, the figures are zero. Tobto. here, in fact, it is supposed to represent like a dozen drib with a zero shot fraction.

To subtract a tenth fraction (or a whole number) by a tenth number, it is necessary to multiply the subdivision and dilnik by the number 10 n, in which number zero more digits after the tenth komi in the dilnik. In such a way, tenths of komi are added in fractions, for which it is necessary to divide. Dali process podіlu zbіgaєtsya s description more.

Graphic display of decimal fractions

Graphically, tens of fractions are displayed behind an additional coordinate line. For this one, one by one, the winds are divided additionally into 10 equal chasms, similarly, as on the lines, centimeters and millimeters are added at the same time. Tse ensures more precisely the fermentation of tens of fractions and the possibility of their objective equalization.

In order for the later handicrafts on single winders to be the same, it is necessary to carefully think over the length of the most single windrow. Vaughn can be such that it is possible to secure the security of the supplementary rozpodіlu.

We have already said that the fractions are blowing primaryі dozens. At the moment, mi trochs have shriveled simple fractions. We found out that the primary fractions are right and wrong. We also recognized that the smallest fractions can be shortened, added up, multiplied and multiplied. I have yet to know that there are such ranks of mixed numbers, as they are composed of a whole and a fractional part.

We have not yet twisted simple fractions to the end. There were a few subtle details, about which we should talk, but even today, we’ll learn more dozens fractions, small scales and tens of fractions are often brought to the bottom. Tobto, when executing a task, it is necessary to practice with both types of shots.

This lesson, perhaps, is foldable and incomprehensible. The whole thing is normal. Such lessons are taught so that they themselves learned them, and did not look over the top.

Viraz the magnitudes of the shotgun

Sometimes it will be easy to show off to a dribbling look. For example, one tenth of a decimeter is written like this:

Tsej visliv means that one decimeter of subdivisions into ten equal parts, and from ten equal parts, one part was taken. And one part out of ten to this particular type more than one centimeter:

Let's look at the attacking butt. Show 6 cm and 3 mm in centimeters for the shotgun.

Also, it is necessary to show 6 cm and 3 mm in centimeters, but in a shotgun look. 6 whole centimeters we already have є:

Ale lost another 3 millimeters. How to show qi 3 milimeters, moreover, in centimeters? Fractions come to the rescue. One centimeter is ten millimeters. Three millimeters - three parts out of ten. And three parts out of ten are recorded like cm

Viraz cm means that one centimeter was subdivided into ten equal parts, and three parts were taken from ten equal parts.

As a result, there are six hundred centimeters and three ten centimeters:

At tsomu 6 shows the number of whole centimeters, and drib - the number of shotguns. Tsey drіb is read like "six cylinders and three ten centimeters".

Fractions, for the banner of yakah, the numbers 10, 100, 1000 can be written down without a banner. On the back, write the whole part, and then the number of the shot part. The number of the part is cremated according to the numeral of the shot part of the Komi.

For example, let's write it down without a banner. We write down the whole part. Number of parts 6

A whole part is written down. Against the backdrop of writing the whole part, we put to whom:

І now we can write down the shotgun number. The numeral of the shot part has the number 3 for the mixed number.

Whether it is a number, as it appears in such a way, it is called decimal fraction.

For this, you can show 6 cm and another 3 mm in centimeters for an additional decimal fraction:

6.3 cm

You will look like this:

Indeed, tens of fractions are themselves primary fractions and mixed numbers. The peculiarity of such shots is that the number 10, 100, 1000 and 10000 stand on the banner of their shot part.

Like a zmishane number, a dozen drib maє tsіlu part and shot. For example, in a mixed number, the number is partly 6, and partly tse.

The tenth fraction has 6.3, the number part is the number 6, and the fractional part is the number of the fraction, that is the number 3.

Buvaє and so, that simple fractions in the banner of such numbers 10, 100, 1000 are given without a whole part. For example, drіb is given without a whole part. To write down such a shot like a dozen, write down 0 first, then put to whom and write down the number of the shot part. A fraction without a banner will be written in the coming rank:

read like "zero two five ten".

Translation of mixed numbers in tens of fractions

If we write down the numbers without a banner, we translate them into tens of fractions. When translating decimal fractions to decimal fractions, it is necessary to know a few moments, we will talk about them at once.

In addition, as the number of the part is written, it is necessary to fix the number of zeros in the standard of the shot part, the number of zeros in the shot part and the number of digits after the Komi in the decimal fraction may be the same. What does it mean? Let's look at the offensive butt:

Spochatku

І it is possible to write down the number of shots and dozens of shots of preparations, but it is necessary to fix the number of zeros at the banner of the shots.

Also, please note the number of zeros in the fractional part of the mixed number. The banner of the shotgun has one zero. So the tenth fraction after Komi will have one digit and this digit will be the numeral of the fractional part of the mixed number, then the number is 2

In this way, when the number is changed into a decimal place, it turns into 3.2.

The tenth drіb reads like this:

"Three tens, two tens"

"Tens" to that in the fractional part of the mixed number there is the number 10.

butt 2. Convert zmishane number to decimal drib.

We write down the whole part and put to whom:

І it is possible to write down the number of the shot fraction and take the tens of fractions 5.3 ale rule to say that after the komi may buti styles of digits and zero zeros in the banner of the shot fraction of the mixed number. And mi bachimo, that the banner of the shot part has two zeros. So our decimal fraction after Komi may have two digits, not one.

In such cases, the number of the shot part needs to be modified three times: add zero before the number, then before the number 3

Now it is possible to translate the tse zmishane number into the tenth drib. We write down the whole part and put to whom:

І write down the shotgun number:

Ten drib 5.03 reads like this:

"Five tsilih, three hundred"

"Sotikh" to that in the banner of the shot part of the mixed number there is the number 100.

example 3. Convert zmishane number to decimal drib.

From the previous applications, we recognized that for a successful conversion of a mixed number into a decimal place, the number of digits in the number of the shot part and the number of zeros in the banner of the shot part may be the same.

Before translating the mixed number into the tens of fractions, it is necessary to change the number of fractions of the shot part, and to work it out in such a way that the number of digits in the number of the shot part and the number of zeros in the banner of the shot part were the same.

We marvel at the number of zeros at the banner of the shotgun. Bachimo, there are three zeros:

Our task is to organize three numbers for the shotgun number. We already have one digit - the whole number 2. Two more digits have been left out. They will be two zeros. Dodamo їх in front of the number 2. As a result, the number of zeros in the znamennik and the number of digits in the numeral will become the same:

Now you can work on translating this mixed number into tenths. We write down the whole part and put to whom:

and immediately write down the number of the shot part

3,002

Bachimo, that the number of digits after Komi and the number of zeros in the banner of the fractional part of the mixed number is the same.

Ten drib 3,002 reads like this:

"Three tsilih, two thousand"

“Thousands” to that in the banner of the shot part of the mixed number there is the number 1000.

Conversion of major fractions to tens of fractions

Forgive the fractions, which have the numbers 10, 100, 1000 or 10000, which can be translated into tens of fractions. Oskіlki at the great fraction of the number of fractions per day, write down 0 in order, then put to whom and write down the number of the fraction of the fraction.

Here, too, the number of zeros for the znamennik, and the number of digits for the number one, can be the same. We should respect that.

example 1.

The number of a part of the day, it means the beginning of the record 0 and set to whom:

Now we marvel at the number of zeros at the bannerman. Bachimo, there's only one zero. І there is one digit in the number book. You can also calmly continue the tenth dream by writing down after the Komi number 5

In the taken decimal fraction 0.5, the number of digits after the Komi and the number of zeros in the banner of the fraction is the same. So drib is translated correctly.

Ten drib 0.5 reads like this:

"Zero Tsilih Five Tens"

butt 2. Convert decimal rub to tenth rub.

The number is part of the day. We write down 0 and put to whom:

Now we marvel at the number of zeros at the bannerman. Bachimo, there are two zeros there. And there is only one digit in the number book. In order to add the number of digits and the number of zeros to the same, add one zero in front of the number 2 in the number book. I'll see you soon. Now the number of zeros for the znamennik is the same as the number of digits for the number one. You can also continue the tenth drib:

In the taken decimal fraction 0.02, the number of digits after the Komi and the number of zeros in the banner of the fraction is the same. So drib is translated correctly.

Tenth drib 0.02 reads like this:

"Zero tsilih, two hundred".

example 3. Convert decimal rub to tenth rub.

Record 0 and set to whom:

Now vvazhaemo kіlkіst nіlіv znamennik shot. Bachimo, there are five zeros there, and there is only one digit in the number book. In order to add the number of zeros to the znamennik, and the number of digits to the number book is the same, it is necessary to add some zeros in the number book before the number 5:

Now the number of zeros for the znamennik is the same as the number of digits for the number one. You can also continue a dozen drib. Write down after the Komi number of fractions

In the taken decimal fraction 0.00005, the number of digits after Komi and the number of zeros in the banner of the fraction is the same. So drib is translated correctly.

Tenth drib 0.00005 reads like this:

"Zero tsilikh, five hundred thousand".

Converting improper fractions to decimal fractions

Wrong drіb tse drіb, which has a bigger number than a banner. Incorrect fractions are used, which have the numbers 10, 100, 1000 or 10000 on the bannerman. Such fractions can be converted into tens of fractions. Ale before the translation of the tens of fractions, in such fractions it is necessary to see the whole part.

example 1.

Drib is an improper fraction. In order to translate such a drіb from a dozen drіb, it is necessary for us to see in front of a new whole part. Guessing, like seeing a whole part of the wrong fractions. Yakshcho zabuli, for the sake of turning around and vivchiti yogo.

Otzhe, we see the whole part in the wrong fraction. Guessing that drіb means rozpodil - in this way, rozpodіl number 112 to the number 10

We marvel at this little one and choose a new number, like a child designer. The number 11 will be the whole part, the number 2 - the number of the shot part, the number 10 - the banner of the shot part.

We took away the zmishane number. Yogo i is translated into decimal drib. And we already know how to translate such numbers to tens fractions. We write down the whole part and put to whom:

Now rahuєmo a lot of zeros at the banner of the shotgun part. Bachimo, there's only one zero. І there is one digit in the number book of the shot part. It means that the number of zeros in the shotgun counter is the same as the number of digits in the shotgun counter. This gives us the opportunity to immediately write down the number of the shot part after the Komi:

In the taken decimal fraction 11.2, the number of digits after the Komi and the number of zeros in the banner of the fraction is the same. So drib is translated correctly.

Meaning an incorrect drop when converted to a tenth drop is converted to 11.2

Ten drib 11.2 reads like this:

"Eleven tsіlih, two tens".

butt 2. Translate incorrect drib to tens drib.

Tse wrong drіb, shards of a number bigger than a banner. Ale її can be translated into a dozen drіb, shards into a banner - the number 100.

We can see a whole part of that shot in front of us. For whom we divide 450 per 100 cuts:

Choose a new zmishane number - take it away. And we already know how to translate mixed numbers to decimal fractions.

We write down the whole part and put to whom:

Now it’s good to have the number of zeros for the shotgun counter and the number of digits for the shotgun counter. Bachimo, that the number of zeros for the znamennik is the same as the number of digits for the number one. This gives us the opportunity to immediately write down the number of the shot part after the Komi:

In the taken decimal fraction 4.50, the number of digits after Komi and the number of zeros in the banner of the fraction is the same. So drib is translated correctly.

Meaning an incorrect drop when converted to a tenth drop is converted to 4.50

When solving problems, as in the example of a decimal fraction, zeros appear, they can be eliminated. Let's and mi vydkinemo zero at our vіdpovіdі. Todi mi otrimayemo 4.5

This is one of the most important features of decimal fractions. Vaughn believes in what is zero, like standing in the end of the shot, not giving any shot to that shot. In other words, tens of fractions 4.50 and 4.5 are equal. Let's put a sign of equality between them:

4,50 = 4,5

Wait for food: why do you think so? Adje looks like 4.50 and 4.5 different fractions. The whole secret lies in the main power fraction, which we have learned earlier. We will try to explain why the decimal fractions 4.50 and 4.5 are added, and after the offensive by those, as it is called "converting the decimal fraction into a mixed number."

Converting a decimal fraction to a mixed number

Whether there is a dozen drіb, there can be translations back in a different number. For whom it is sufficient to read tens of fractions. For example, we translate 6.3 for a different number. 6:3 for six hundred and three tenths. Write down six times in a row:

i order three tenths:

butt 2. Convert decimal drib 3,002 y zmishane number

3,002 three quarters and two thousandths. Write down three numbers

and entrusted to write down two thousand:

example 3. Convert decimal drib 4.50 to zmishane number

4.50 tse chotiri tsilih and fifty hundreds. We write down everything

and order f'fifty sotikh:

Before speech, let's guess the rest of the butt from the front ones. We said that tens of fractions are 4.50 and 4.5 are equal. So we said that zero can be found. Let's try to bring that dozens of 4.50 and 4.5 equal. For whom we can translate offensive tens of fractions to mixed numbers.

After the transfer in zmishane, the number of tenth rub 4.50 is charged up to , and the tenth ruble 4.5 is rolled up to

Maybe two mixed numbers i. Let's translate the number of mixed numbers to improper fractions:

Now maybe two fractions. The hour has come to guess the main power of the fraction, as if to say that when multiplying (the number of digits) and the banner of the fraction, the same number does not change the value of the fraction.

Let's split the first drop by 10

They took it away, but another drib. Mean and equal to each other and equal to the same meaning:

Try on the calculator to divide the odds 450 by 100, and then 45 by 10. A funny thing is the viide.

Translation of the tenth fraction of the greatest fraction

Whether there are dozens of drіb can be back translations from the greatest drіb. For whom I am still enough to read tens of fractions. For example, let's translate 0.3 for the greatest drіb. 0.3 price zero or two and three tenths. We write down zero numbers:

i exponent three decimal 0 . Zero is not written down by tradition, so the residual will be not 0, but simply.

butt 2. Convert decimal fraction 0.02 to the greatest fraction.

0.02 price zero two hundred Zero is not written down, then two hundredths are written down

example 3. Shift 0.00005 to the greatest fraction

0.00005 is the price of zero and five hundred thousandths. Zero is not written down, five hundred thousandths are immediately written down

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Remember, like in the very first lesson about decimal fractions, I showed you how to understand numerical fractions, which are not represented by decimal fractions (divinary lesson “Decimal Fractions”)? Mishche learned to lay out the banners of fractions into multipliers, to reconsider, there are no numbers of double types 2 and 5.

So the axis: I've come across. And today we learn to translate absolutely whether there is a numerical difference in tens. At the same time, we get to know a whole class of shots from an inexhaustible significant part.

Periodic tenth drіb - whether there be a tens of drіb, for which:

1. Significant part is added up from anonymous numbers;
2. Through the sing intervals, the digits of the significant part are repeated.

A set of numbers that are repeated, from which they add up significant part, It is called a periodic partial fraction, and the number of digits in this set is a period fraction. Reshta against a significant part, which is not repeated, is called a non-periodic part.

Oskіlki vyznachen rich, varto reportedly look at such fractions:

Tsey drіb zustrichaetsya in the zavdannya most. Non-periodic part: 0; periodic part: 3; Dovzhina period: 1.

Non-periodic part: 0.58; periodic part: 3; Dovzhina period: new 1.

Non-periodic part: 1; periodic part: 54; date period: 2.

Non-periodic part: 0; periodic part: 641025; dovzhina period: 6. For the clarity of the parts that are repeated, one in the same gap - for whom the decision is not so obov'yazkovo.

Non-periodic part: 3066; periodic part: 6; Dovzhina period: 1.

Like a bachite, the designation of a periodic fraction is based on understanding significant part of the number. To that yakscho ve zabuli, sho tse take, I recommend repeating - div. lesson " ".

Transition to periodic decimal fraction

Let's look at the most remarkable sight of a / b. We lay out the banner on simple multipliers. Two options are possible:

1. The layout has more than 2 and 5 multipliers. Qi fractions are easy to point up to tens - divs. Lesson "Decimal Fractions" So do not chirp us;
2. The spread is present, crim 2 and 5. In this case, the drib is unrepresentable in the look of the tenth, but then you can add a periodic tens of drib.

To set a periodic decimal point, you need to know both periodic and non-periodic parts. Yak? Translate drib from the wrong ones, and then divide the number on the flag in a little bundle.

If so, it should be like this:

1. Spread out on the cob whole part yakscho won є;
2. Possibly, there will be a sprinkling of numbers after the tenth point;
3. After a deaky hour, the numbers will start repeat.

From i all! Repeating numbers after the tenth point are signified by a periodic part, and those that stand in front are non-periodic.

Manager. Converting decimal fractions to periodic tens:

All fractions without a whole part, so we just divide the number on the banner "kutochkoy":

Yak bachimo, the leftovers are repeated. Let's write down the difference for the "correct" look: 1.733...=1.7(3).

Drib comes out through war: 0.5833 ... = 0.58(3).

Recorded for normal looking: 4.0909...=4,(09).

Take away drib: 0.4141...=0,(41).

Transition from a periodic decimal fraction to a decimal fraction

Let's look at the periodic decimal point X = abc (a 1 b 1 c 1). It is necessary to translate її into the classic "two-top". For whom we are looking for simple short cuts:

1. Find the period of the fraction, tobto. cheer up, how many numbers are in the periodic part. Let it be the number k;
2. Find the value of virusase X 10 k. Ceriously destroying the tenth point for the last period right-handed - div. lesson "Multiplication and division of tens of fractions";
3. On the third day of the day, you need to take out the virus. At what periodical part "saluted" and lost splendid drіb;
4. In otrimanomu equal to know X. Uсі tens fractions are translatable in simple.

Manager. Convert to the largest improper fraction of a number:

• 9,(6);
• 32,(39);
• 0,30(5);
• 0,(2475).

Practice with the first fraction: X \u003d 9, (6) \u003d 9.666.

The arms have less than one digit, so the period k = 1. Then we multiply this drib by 10 k = 10 1 = 10. Maybe:

10X = 10 9.6666... ​​= 96.666...

Vіdnіmaєmo vihіdny drіb і rozv'yazuєmo rіvnyannya:

10X - X = 96.666 ... - 9.666 ... = 96 - 9 = 87;
9X=87;
X = 87/9 = 29/3.

Now let's take a look at another fraction. Also, X = 32, (39) = 32.393939.

Period k = 2, so we multiply everything by 10 k = 10 2 = 100:

100X = 100 32.393939 ... = 3239.3939 ...

Anew I see the weekend drіb and virishuєmo equal:

100X - X = 3239.3939 ... - 32.3939 ... = 3239 - 32 = 3207;
99X = 3207;
X = 3207/99 = 1069/33.

Let's get down to the third fraction: X = 0.30(5) = 0.30555 ... The scheme is the same, for that I'll just point the tabs:

Period k = 1 ⇒ multiply everything by 10 k = 10 1 = 10;

10X = 10 0.30555... = 3.05555...
10X - X = 3.0555 ... - 0.305555 ... = 2.75 = 11/4;
9X = 11/4;
X = (11/4): 9 = 11/36.

Nareshti, rest drіb: X = 0, (2475) = 0.2475 2475 ... Well, I know, for the sake of clarity, the periodic part of the Kremlin has one in one gap. Maemo:

k = 4 ⇒ 10 k = 10 4 = 10,000;
10000X = 10000 0.2475 2475 = 2475.2475 ...
10,000X - X = 2475.2475 ... - 0.2475 2475 ... = 2475;
9999X = 2475;
X = 2475: 9999 = 25/101.