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What does it mean to round to the nearest whole number? How to round decimals

Methods

IN different areas may be applied various methods rounding. In all these methods, “extra” signs are reset (discarded), and the sign preceding them is adjusted according to some rule.

  • Round to the nearest integer(English) rounding) - the most commonly used rounding, in which a number is rounded to an integer, the modulus of the difference with which this number has a minimum. In general, when a number in the decimal system is rounded to the Nth decimal place, the rule can be formulated as follows:
    • If N+1 sign< 5 , then the Nth sign is retained, and N+1 and all subsequent ones are reset to zero;
    • If N+1 character ≥ 5, then the Nth sign is increased by one, and N+1 and all subsequent ones are reset to zero;
    For example: 11.9 → 12; −0.9 → −1; −1,1 → −1; 2.5 → 3.
  • Rounding down modulo(round to zero, integer English) fix, truncate, integer) is the “simplest” rounding, since after zeroing out the “extra” signs, the previous sign is retained. For example, 11.9 → 11; −0.9 → 0; −1,1 → −1).
  • Round up(round to +∞, round up, English) ceiling) - if the zeroing signs are not equal to zero, the previous sign is increased by one if the number is positive, or retained if the number is negative. In economic jargon - rounding in favor of the seller, creditor(person receiving money). In particular, 2.6 → 3, −2.6 → −2.
  • Round down(round to −∞, round down, English. floor) - if the zeroing signs are not equal to zero, the previous sign is retained if the number is positive, or increased by one if the number is negative. In economic jargon - rounding in favor of the buyer, debtor(the person giving the money). Here 2.6 → 2, −2.6 → −3.
  • Rounding up modulo(round toward infinity, round away from zero) is a relatively rarely used form of rounding. If the zeroing signs are not equal to zero, the preceding sign is increased by one.

Options for rounding 0.5 to the nearest integer

Rounding rules require a separate description for the special case when (N+1)th digit = 5 and subsequent digits are zero. If in all other cases rounding to the nearest integer provides a smaller rounding error, then this particular case is characterized by the fact that for a single rounding it is formally indifferent whether it is done “up” or “down” - in both cases an error of exactly 1/2 of the least significant digit is introduced . There are the following options for the rounding to the nearest integer rule for this case:

  • Mathematical rounding- rounding is always upward (the previous digit is always increased by one).
  • Bank rounding(English) banker's rounding) - rounding for this case occurs to the nearest even number, that is, 2.5 → 2, 3.5 → 4.
  • Random rounding- rounding occurs to the nearest or lower big side in random order, but with equal probability (can be used in statistics).
  • Alternate rounding- rounding occurs downward or upward alternately.

In all cases, when the (N+1)th digit is not equal to 5 or subsequent digits are not equal to zero, rounding occurs according to the usual rules: 2.49 → 2; 2.51 → 3.

Mathematical rounding simply formally corresponds general rule rounding (see above). Its disadvantage is that when rounding a large number of values, accumulation may occur. rounding errors. Typical example: rounding to whole rubles sums of money. So, if in a register of 10,000 lines there are 100 lines with amounts containing the value of 50 in kopecks (and this is a very realistic estimate), then when all such lines are rounded “up”, the “total” amount for the rounded register will be 50 rubles more than the exact one .

The other three options were invented precisely in order to reduce the overall error of the sum when rounding large quantity values. Rounding “to the nearest even” is based on the assumption that when large number For rounded values ​​that have 0.5 in the remainder, on average half will be to the left and half to the right of the nearest even number, thus canceling out rounding errors. Strictly speaking, this assumption is true only when the set of numbers being rounded has the properties of a random series, which is usually true in accounting applications where we are talking about prices, account amounts, and so on. If the assumption is violated, then rounding “to even” can lead to systematic errors. For such cases, the following two methods work better.

The last two rounding options ensure that approximately half special meanings will be rounded in one direction, half in the other. But the implementation of such methods in practice requires additional efforts to organize the computational process.

Applications

Rounding is used to work with numbers within the number of decimal places that corresponds to the actual accuracy of the calculation parameters (if these values ​​represent real quantities measured in one way or another), the actually achievable accuracy of the calculations, or the desired accuracy of the result. In the past, rounding intermediate values ​​and results was of practical importance (since when calculating on paper or using primitive devices such as the abacus, taking into account extra decimal places can seriously increase the amount of work). Now it remains an element of scientific and engineering culture. In accounting applications, in addition, the use of rounding, including intermediate rounding, may be required to protect against computational errors associated with the finite capacity of computing devices.

Using rounding when working with numbers of limited precision

Real physical quantities are always measured with a certain finite accuracy, which depends on the instruments and measurement methods and is estimated by the maximum relative or absolute deviation of the unknown real value from the measured one, which in the decimal representation of the value corresponds to either a certain number of significant digits or a certain position in the recording of the number, all the numbers after (to the right) of which are insignificant (are within the measurement error). The measured parameters themselves are recorded with such a number of characters that all figures are reliable, perhaps the last one is doubtful. The error during mathematical operations with numbers of limited accuracy is preserved and changes according to known mathematical laws, therefore, when intermediate values ​​and results with a large number of digits appear in further calculations, only some of these digits are significant. The remaining numbers, while present in the values, do not actually reflect any physical reality and only take up time for calculations. As a result, intermediate values ​​and results in calculations with limited accuracy are rounded to the number of decimal places that reflects the actual accuracy of the obtained values. In practice, it is usually recommended to store one more digit in intermediate values ​​for long "chain" manual calculations. When using a computer, intermediate rounding in scientific and technical applications most often loses its meaning, and only the result is rounded.

So, for example, if a force of 5815 gf is given with an accuracy of a gram of force and the arm length is 1.4 m with an accuracy of a centimeter, then the moment of force in kgf according to the formula, in the case of a formal calculation with all signs, will be equal to: 5.815 kgf 1.4 m = 8.141 kgf m. However, if we take into account the measurement error, we find that the maximum relative error of the first value is 1/5815 ≈ 1,7 10 −4 , second - 1/140 ≈ 7,1 10 −3 , the relative error of the result according to the error rule of the multiplication operation (when multiplying approximate values, the relative errors add up) will be 7,3 10 −3 , which corresponds to the maximum absolute error of the result ±0.059 kgf m! That is, in reality, taking into account the error, the result can range from 8.082 to 8.200 kgf m, thus, in the calculated value of 8.141 kgf m, only the first figure is completely reliable, even the second is already doubtful! It would be correct to round the calculation result to the first dubious digit, that is, to tenths: 8.1 kgf m, or, if it is necessary to more accurately indicate the scope of the error, present it in the form rounded to one or two decimal places indicating the error: 8.14 ± 0.06 kgf m.

Rules of thumb for arithmetic with rounding

In cases where there is no need to accurately take into account computational errors, but only need to approximately estimate the amount exact numbers As a result of calculation using the formula, you can use the set simple rules rounded calculations:

  1. All original values ​​are rounded to the actual measurement accuracy and recorded with the appropriate number of significant figures, so that decimal notation all figures were reliable (it is allowed that last digit was doubtful). If necessary, values ​​are written with significant right-hand zeros so that the record indicates the actual number of reliable characters (for example, if a length of 1 m is actually measured to the nearest centimeter, write “1.00 m” to show that two characters are reliable in the record after the decimal point), or the accuracy is explicitly indicated (for example, 2500 ± 5 m - here only tens are reliable, and should be rounded to them).
  2. Intermediate values ​​are rounded with one “spare” digit.
  3. When adding and subtracting, the result is rounded to the last decimal place of the least accurate parameter (for example, when calculating the value 1.00 m + 1.5 m + 0.075 m, the result is rounded to the nearest tenth of a meter, that is, to 2.6 m). In this case, it is recommended to perform calculations in such an order as to avoid subtracting numbers that are close in magnitude and to perform operations on numbers, if possible, in increasing order of their modules.
  4. When multiplying and dividing, the result is rounded to smallest number significant digits that the parameters have (for example, when calculating the speed uniform motion bodies at a distance of 2.5 10 2 m, for 600 s the result should be rounded to 4.2 m/s, since distance has two digits, and time has three, assuming that all digits in the record are significant).
  5. When calculating the function value f(x) it is required to estimate the modulus of the derivative of this function in the vicinity of the calculation point. If (|f"(x)| ≤ 1), then the function result is accurate to the same decimal place as the argument. Otherwise, the result contains fewer exact decimal places by the amount log 10 (|f"(x)|), rounded up to the nearest whole number.

Despite the lack of rigor, the above rules work quite well in practice, in particular, because high probability mutual cancellation of errors, which is usually not taken into account when accurately accounting for errors.

Errors

Abuse of non-round numbers is quite common. For example:

  • Numbers that have low accuracy are recorded in unrounded form. In statistics: if 4 people out of 17 answered “yes”, then they write “23.5%” (while “24%” is correct).
  • Users of pointer instruments sometimes think like this: “the needle stopped between 5.5 and 6 closer to 6, let it be 5.8” - this is also prohibited (the calibration of the device usually corresponds to its real accuracy). In this case, you should say “5.5” or “6”.

See also

  • Processing observations
  • Rounding errors

Notes

Literature

  • Henry S. Warren, Jr. Chapter 3. Rounding to powers of 2// Algorithmic tricks for programmers = Hacker's Delight. - M.: Williams, 2007. - P. 288. - ISBN 0-201-91465-4

In some cases, the exact number when dividing a certain amount it is impossible to determine a specific number in principle. For example, when dividing 10 by 3, we get 3.3333333333.....3, that is, this number cannot be used to count specific items in other situations. Then this number should be reduced to a certain digit, for example, to an integer or to a number with a decimal place. If we reduce 3.3333333333…..3 to an integer, we get 3, and if we reduce 3.3333333333…..3 to a number with a decimal place, we get 3.3.

Rounding rules

What is rounding? This is discarding a few digits that are the last in the series of an exact number. So, following our example, we discarded all the last digits to get the integer (3) and discarded the digits, leaving only the tens places (3,3). The number can be rounded to hundredths and thousandths, ten thousandths and other numbers. It all depends on how accurate the number needs to be. For example, in the manufacture medical supplies, the amount of each of the ingredients of the medicine is taken with the greatest accuracy, since even a thousandth of a gram can lead to fatal outcome. If it is necessary to calculate the progress of students at school, then most often a number with a decimal or hundredth place is used.

Let's look at another example where rounding rules apply. For example, there is a number 3.583333 that needs to be rounded to thousandths - after rounding, we should be left with three digits after the decimal point, that is, the result will be the number 3.583. If we round this number to tenths, then we get not 3.5, but 3.6, since after “5” there is the number “8”, which is already equal to “10” during rounding. Thus, following the rules of rounding numbers, you need to know that if the digits are greater than "5", then the last digit to be stored will be increased by 1. If there is a digit less than "5", the last digit to be stored remains unchanged. These rules for rounding numbers apply regardless of whether to a whole number or to tens, hundredths, etc. you need to round the number.

In most cases, when you need to round a number in which the last digit is “5,” this process is not performed correctly. But there is also a rounding rule that applies specifically to such cases. Let's look at an example. It is necessary to round the number 3.25 to the nearest tenth. Applying the rules for rounding numbers, we get the result 3.2. That is, if there is no digit after “five” or there is a zero, then the last digit remains unchanged, but only if it is even - in our case, “2” is an even digit. If we were to round 3.35, the result would be 3.4. Because, in accordance with the rules of rounding, if there is an odd digit before the “5” that must be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after the “5”. In many cases, simplified rules can be applied, according to which, if the last stored digit is followed by the values ​​of digits from 0 to 4, the stored digit does not change. If there are other digits, the last digit is increased by 1.

In approximate calculations, it is often necessary to round some numbers, both approximate and exact, that is, remove one or more ending digits. To ensure that an individual rounded number is as close as possible to the number being rounded, certain rules must be followed.

If the first of the separated digits is greater than the number 5, then the last of the remaining digits is amplified, in other words, increased by one. Gain is also assumed when the first of the removed digits is equal to 5, and after it there is one or a number of significant digits.

The number 25.863 is rounded down as – 25.9. IN in this case the digit 8 will be strengthened to 9, since the first digit cut off is 6, greater than 5.

The number 45.254 is rounded down as – 45.3. Here the digit 2 will be boosted to 3 since the first digit cut off is 5 and followed by the significant digit 1.

If the first of the cut-off digits is less than 5, then no amplification is performed.

The number 46.48 is rounded down as – 46. The number 46 is closest to the number being rounded than 47.

If the digit 5 ​​is cut off and there are no significant digits behind it, then rounding is performed to the nearest even number, in other words, the last digit left remains unchanged if it is even, and is strengthened if it is odd.

The number 0.0465 is rounded down as – 0.046. In this case, no amplification is done, since the last digit left, 6, is even.

The number 0.935 is rounded down as – 0.94. The last digit left, 3, is strengthened since it is odd.

Rounding numbers

Numbers are rounded when complete accuracy is not needed or possible.

Round number to a certain number (sign), means replacing it with a number close in value with zeros at the end.

Natural numbers are rounded to tens, hundreds, thousands, etc. Names of numbers in ranks natural number You can remember the topic of natural numbers.

Depending on the digit to which the number needs to be rounded, we replace the digit in the units, tens, etc. digits with zeros.

If a number is rounded to tens, then we replace the digit in the ones place with zeros.

If a number is rounded to the nearest hundred, the zero must be in both the units place and the tens place.

The number obtained by rounding is called an approximate value of the given number.

Record the rounding result after special sign"≈". This sign reads “approximately equal.”

When rounding a natural number to any place value, you must use rounding rules.

  1. Underline the digit of the place to which the number should be rounded.
  2. Separate all numbers to the right of this digit with a vertical line.
  3. If there is a digit 0, 1, 2, 3 or 4 to the right of the underlined digit, then all digits that are separated to the right are replaced with zeros. We leave the digit to which we rounded unchanged.
  4. If there is a digit 5, 6, 7, 8 or 9 to the right of the underlined digit, then all digits that are separated to the right are replaced with zeros, and 1 is added to the place digit to which it was rounded.

Let's explain with an example. Let's round 57,861 to thousands. Let's follow the first two points of the rounding rules.

After the underlined digit there is the number 8, which means we add 1 to the thousand digit (for us it is 7), and replace all digits separated by a vertical bar with zeros.

Now let's round 756,485 to hundreds.

Let's round 364 to tens.

3 6 |4 ≈ 360 - in the units place there is 4, so we leave 6 in the tens place unchanged.

On the number line, the number 364 is enclosed between two "round" numbers 360 and 370. These two numbers are called approximations of the number 364, accurate to tens.

The number 360 is approximate missing value, and the number 370 is approximate value in excess.

In our case, rounding 364 to tens, we got 360 - an approximate value with a disadvantage.

Rounded results are often written without the zeros, adding the abbreviation "thousands." (thousand), "million" (million) and "billion." (billion).

  • 8,659,000 = 8,659 thousand
  • 3,000,000 = 3 million.

Rounding is also used to estimate the answer in calculations.

Before making an exact calculation, we will make an estimate of the answer, rounding the factors to the highest digit.

794 52 ≈ 800 50 ≈ 40,000

We conclude that the answer will be close to 40,000.

794 52 = 41,228

Similarly, you can make estimates by rounding when dividing numbers.

In some cases, the exact number when dividing a certain amount by a specific number cannot be determined in principle. For example, when dividing 10 by 3, we get 3.3333333333.....3, that is, this number cannot be used to count specific items in other situations. Then this number should be reduced to a certain digit, for example, to an integer or to a number with a decimal place. If we reduce 3.3333333333…..3 to an integer, we get 3, and if we reduce 3.3333333333…..3 to a number with a decimal place, we get 3.3.

Rounding rules

What is rounding? This is discarding a few digits that are the last in the series of an exact number. So, following our example, we discarded all the last digits to get the integer (3) and discarded the digits, leaving only the tens places (3,3). The number can be rounded to hundredths and thousandths, ten thousandths and other numbers. It all depends on how accurate the number needs to be. For example, in the manufacture of medicines, the quantity of each of the ingredients of the medicine is taken with the greatest precision, since even a thousandth of a gram can be fatal. If it is necessary to calculate the progress of students at school, then most often a number with a decimal or hundredth place is used.

Let's look at another example where rounding rules apply. For example, there is a number 3.583333 that needs to be rounded to thousandths - after rounding, we should have three digits after the decimal point, that is, the result will be the number 3.583. If we round this number to tenths, then we get not 3.5, but 3.6, since after “5” there is the number “8”, which is already equal to “10” during rounding. Thus, following the rules of rounding numbers, you need to know that if the digits are greater than "5", then the last digit to be stored will be increased by 1. If there is a digit less than "5", the last digit to be stored remains unchanged. These rules for rounding numbers apply regardless of whether to a whole number or to tens, hundredths, etc. you need to round the number.

In most cases, when you need to round a number in which the last digit is “5,” this process is not performed correctly. But there is also a rounding rule that applies specifically to such cases. Let's look at an example. It is necessary to round the number 3.25 to the nearest tenth. Applying the rules for rounding numbers, we get the result 3.2. That is, if there is no digit after “five” or there is a zero, then the last digit remains unchanged, but only if it is even - in our case, “2” is an even digit. If we were to round 3.35, the result would be 3.4. Because, in accordance with the rules of rounding, if there is an odd digit before the “5” that must be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after the “5”. In many cases, simplified rules can be applied, according to which, if the last stored digit is followed by the values ​​of digits from 0 to 4, the stored digit does not change. If there are other digits, the last digit is increased by 1.

5.5.7. Rounding numbers

To round a number to any digit, we underline the digit of this digit, and then we replace all the digits after the underlined one with zeros, and if they are after the decimal point, we discard them. If the first digit replaced by a zero or discarded is 0, 1, 2, 3 or 4, then the underlined number leave unchanged. If the first digit replaced by a zero or discarded is 5, 6, 7, 8 or 9, then the underlined number increase by 1.

Examples.

Round to whole numbers:

1) 12,5; 2) 28,49; 3) 0,672; 4) 547,96; 5) 3,71.

Solution. We underline the number in the units (integer) place and look at the number behind it. If this is the number 0, 1, 2, 3 or 4, then we leave the underlined number unchanged, and discard all the numbers after it. If the underlined number is followed by the number 5 or 6 or 7 or 8 or 9, then we will increase the underlined number by one.

1) 1 2 ,5≈13;

2) 2 8 ,49≈28;

3) 0 ,672≈1;

4) 54 7 ,96≈548;

5) 3 ,71≈4.

Round to the nearest tenth:

6) 0, 246; 7) 41,253; 8) 3,81; 9) 123,4567; 10) 18,962.

Solution. We underline the number in the tenths place, and then proceed according to the rule: we discard everything after the underlined number. If the underlined number was followed by the number 0 or 1 or 2 or 3 or 4, then we do not change the underlined number. If the underlined number was followed by the number 5 or 6 or 7 or 8 or 9, then the underlined number will be increased by 1.

6) 0, 2 46≈0,2;

7) 41, 2 53≈41,3;

8) 3, 8 1≈3,8;

9) 123, 4 567≈123,5;

10) 18.9 62≈19.0. Behind nine there is a six, therefore, we increase nine by 1. (9+1=10) we write zero, 1 goes to the next digit and it will be 19. We just can’t write 19 in the answer, since it should be clear that we rounded to tenths - the number must be in the tenths place. Therefore, the answer is: 19.0.

Round to the nearest hundredth:

11) 2, 045; 12) 32,093; 13) 0, 7689; 14) 543, 008; 15) 67, 382.

Solution. We underline the digit in the hundredths place and, depending on which digit comes after the underlined one, leave the underlined digit unchanged (if it is followed by 0, 1, 2, 3 or 4) or increase the underlined digit by 1 (if it is followed by 5, 6, 7, 8 or 9).

11) 2, 0 4 5≈2,05;

12) 32,0 9 3≈32,09;

13) 0, 7 6 89≈0,77;

14) 543, 0 0 8≈543,01;

15) 67, 3 8 2≈67,38.

Important: the last answer should contain a number in the digit to which you rounded.

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How to round a number to a whole number

Applying the rule for rounding numbers, consider specific examples How to round a number to a whole number.

Rule for rounding a number to a whole number

To round a number to an integer (or round a number to units), you need to discard the comma and all numbers after the decimal point.

If the first digit discarded is 0, 1, 2, 3 or 4, then the number will not change.

If the first digit dropped is 5, 6, 7, 8, or 9, the previous digit must be increased by one.

Round the number to the nearest integer:

To round a number to an integer, discard the comma and all numbers after it. Since the first digit discarded is 2, we do not change the previous digit. They read: “eighty-six point twenty-four hundredths is approximately equal to eighty-six whole.”

When rounding a number to the nearest integer, we discard the comma and all numbers following it. Since the first of the discarded digits is equal to 8, we increase the previous one by one. They read: “Two hundred and seventy-four point eight hundred and thirty-nine thousandths is approximately equal to two hundred and seventy-five whole.”

When rounding a number to the nearest integer, we discard the comma and all numbers following it. Since the first of the discarded digits is 5, we increase the previous one by one. They read: “Zero point fifty-two hundredths is approximately equal to one point.”

We discard the comma and all numbers after it. The first of the discarded digits is 3, so we do not change the previous digit. They read: “Zero point three ninety-seven thousandths is approximately equal to zero point.”

The first of the discarded digits is 7, which means that the digit in front of it is increased by one. They read: “Thirty-nine point seven hundred and four thousandths is approximately equal to forty whole.” And a couple more examples for rounding numbers to integers:

27 Comments

Wrong theory about if the number 46.5 is not 47 but 46, this is also called bank rounding to the nearest even number, it is rounded if there is 5 after the decimal point and there is no number after it

Dear ShS! Perhaps(?), in banks rounding occurs according to different rules. I don't know, I don't work in a bank. This site talks about the rules that apply in mathematics.

how to round the number 6.9?

To round a number to an integer, you need to discard all the numbers after the decimal point. We discard 9, so the previous number should be increased by one. This means that 6.9 is approximately equal to seven whole numbers.

In fact, the figure does not really increase if there is a 5 after the decimal point in any financial institution

Hm. In that case financial institutions in matters of rounding, they are guided not by the laws of mathematics, but by their own considerations.

Tell me how to round 46.466667. Confused

If you need to round a number to an integer, then you need to discard all the digits after the decimal point. The first of the discarded digits is 4, so we do not change the previous digit:

Dear Svetlana Ivanovna. You are not very familiar with the rules of mathematics.

Rule. If the digit 5 ​​is discarded and there are no significant digits behind it, then rounding is done to the nearest even number, i.e., the last digit retained is left unchanged if it is even and strengthened if it is odd.

And Accordingly: Rounding the number 0.0465 to the third decimal place, we write 0.046. We do not make any gains, since the last digit saved, 6, is even. The number 0.046 is as close to this as 0.047.

Dear guest! Let it be known that in mathematics there are numbers for rounding various ways rounding. At school they study one of them, which consists in discarding the lower digits of a number. I’m glad for you that you know another way, but it would be nice not to forget your school knowledge.

Thank you very much! It was necessary to round 349.92. That turns out to be 350. Thanks for the rule?

how to round 5499.8 correctly?

If we are talking about rounding to a whole number, then discard all numbers after the decimal point. The discarded digit is 8, therefore, we increase the previous one by one. This means that 5499.8 is approximately equal to 5500 integers.

Good day!
Now this question arose:
There are three numbers: 60.56% 11.73% and 27.71% How to round up to whole numbers? So that the total remains 100. If you simply round, then 61+12+28=101 There is a discrepancy. (If, as you wrote, using the “banking” method, in this case it will work, but in the case of, for example, 60.5% and 39.5%, something will fall again - we will lose 1%.) What should I do?

ABOUT! the method from “guest 07/02/2015 12:11″ helped
Thank you"

I don’t know, they taught me this at school:
1.5 => 1
1.6 => 2
1.51 => 2
1.51 => 1.6

Perhaps you were taught this way.

0.855 to hundredths please help

0.855≈0.86 (5 is discarded, the previous digit is increased by 1).

Round 2.465 to a whole number

2.465≈2 (the first discarded digit is 4. Therefore, we leave the previous one unchanged).

How to round 2.4456 to a whole number?

2.4456 ≈ 2 (since the first digit discarded is 4, we leave the previous digit unchanged).

Based on the rounding rules: 1.45=1.5=2, therefore 1.45=2. 1,(4)5 = 2. Is this true?

No. If you need to round 1.45 to a whole number, discard the first digit after the decimal point. Since this is 4, we do not change the previous digit. Thus, 1.45≈1.

Let's look at examples of how to round numbers to tenths using rounding rules.

Rule for rounding numbers to tenths.

To round a decimal fraction to tenths, you must leave only one digit after the decimal point and discard all other digits that follow it.

If the first of the discarded digits is 0, 1, 2, 3 or 4, then the previous digit is not changed.

If the first of the discarded digits is 5, 6, 7, 8 or 9, then we increase the previous digit by one.

Examples.

Round to the nearest tenth:

To round a number to tenths, leave the first digit after the decimal point and discard the rest. Since the first digit discarded is 5, we increase the previous digit by one. They read: “Twenty-three point seven five hundredths is approximately equal to twenty three point eight tenths.”

To round this number to tenths, leave only the first digit after the decimal point and discard the rest. The first digit discarded is 1, so we do not change the previous digit. They read: “Three hundred forty-eight point thirty-one hundredths is approximately equal to three hundred forty-one point three tenths.”

When rounding to tenths, we leave one digit after the decimal point and discard the rest. The first of the discarded digits is 6, which means we increase the previous one by one. They read: “Forty-nine point nine, nine hundred sixty-two thousandths is approximately equal to fifty point zero, zero tenths.”

We round to the nearest tenth, so after the decimal point we leave only the first of the digits, and discard the rest. The first of the discarded digits is 4, which means we leave the previous digit unchanged. They read: “Seven point twenty-eight thousandths is approximately equal to seven point zero tenths.”

To round a given number to tenths, leave one digit after the decimal point, and discard all those following it. Since the first digit discarded is 7, therefore, we add one to the previous one. They read: “Fifty-six point eight thousand seven hundred six ten thousandths is approximately equal to fifty six point nine tenths.”

And a couple more examples for rounding to tenths:

If displaying unnecessary digits causes ###### signs to appear, or if microscopic precision is not needed, change the cell format so that only the necessary decimal places are displayed.

Or if you want to round a number to the nearest major place, such as thousandths, hundredths, tenths, or ones, use the function in the formula.

Using a button

    Select the cells you want to format.

    On the tab Home select team Increase bit depth or Decrease bit depth to display more or fewer decimal places.

By using built-in number format

    On the tab Home in the group Number Click the arrow next to the list of number formats and select Other number formats.

    In the field Number of decimal places enter the number of decimal places you want to display.

Using a function in a formula

Round the number to the required number of digits using the ROUND function. This function only has two argument(arguments are pieces of data needed to execute a formula).

    The first argument is the number to be rounded. It can be a cell reference or a number.

    The second argument is the number of digits to which the number should be rounded.

Let's say cell A1 contains the number 823,7825 . Here's how to round it up.

    To round to the nearest thousand And

    • Enter =ROUND(A1,-3), which is equal 100 0

      The number 823.7825 is closer to 1000 than to 0 (0 is a multiple of 1000)

      In this case it is used negative number, since rounding must take place to the left of the decimal point. The same number is used in the next two formulas, which round to the nearest hundreds and tens.

    To round to the nearest hundred

    • Enter =ROUND(A1,-2), which is equal 800

      The number 800 is closer to 823.7825 than to 900. Probably everything is clear to you now.

    To round to the nearest dozens

    • Enter =ROUND(A1,-1), which is equal 820

    To round to the nearest units

    • Enter =ROUND(A1,0), which is equal 824

      Use zero to round a number to the nearest one.

    To round to the nearest tenths

    • Enter =ROUND(A1,1), which is equal 823,8

      In this case, use a positive number to round the number to the required number of digits. The same goes for the following two formulas, which round to hundredths and thousandths.

    To round to the nearest hundredths

    • Enter =ROUND(A1,2), which is equal to 823.78

    To round to the nearest thousandths

    • Enter =ROUND(A1,3), which is equal to 823.783

Round a number up using the ROUND UP function. It works exactly the same as the ROUND function, except that it always rounds the number up. For example, if you need to round the number 3.2 to zero digits:

    =ROUNDUP(3,2,0), which is equal to 4

Round a number down using the ROUNDDOWN function. It works exactly the same as the ROUND function, except that it always rounds the number down. For example, you need to round the number 3.14159 to three digits:

    =ROUNDBOTTOM(3.14159,3), which is equal to 3.141