How to round to hundredths of whole numbers is a rule. How to round decimals

Suppose that you want to round a number to the nearest integer, since decimal values are not important to you, or you want to represent the number as a power of 10 to make approximate calculations easier. There are several ways to round numbers.

Change the number of decimal places without changing the value

On the sheet

Inline numeric format

Round a number up

Round a number to the nearest value

Round a number to the nearest fractional value

Round a number to a specified number of significant digits

Significant places are places that affect the precision of a number.

The examples in this section use the functions ROUND, ROUNDUP and ROUNDDOWN... They show how to round positive, negative, whole, and decimal numbers, but the examples provided cover only a small fraction of the possible situations.

The list below contains general rules to consider when rounding numbers to the specified number of significant digits. You can experiment with rounding functions and substitute eigenvalues and parameters to get a number with the required number of significant digits.

Rounded negative numbers are primarily converted to absolute values (values without a minus sign). After rounding, the minus sign is reapplied. While it may seem counterintuitive, this is how rounding is done. For example, when using the function ROUNDDOWN to round -889 to 2 significant digits, the result is -880. First, -889 is converted to an absolute value (889). This value is then rounded to two significant digits (880). The minus sign is then reapplied, resulting in -880.

When applied to a positive number, the function ROUNDDOWN it always rounds down, and when the function is applied ROUNDUP- up.

Function ROUND rounds fractional numbers as follows: if the fractional part is greater than or equal to 0.5, the number is rounded up. If the fractional part is less than 0.5, the number is rounded down.

Function ROUND rounds whole numbers up or down in the same way, using 5 instead of 0.5.

In general, when rounding a number without a fractional part (an integer), you must subtract the length of the number from the required number of significant digits. For example, to round 2345678 down to 3 significant digits, use the function ROUNDDOWN with parameter -4: = ROUNDDOWN (2345678, -4)... This rounds the number to 2340000, where the "234" part represents significant digits.

Round a number to a specified multiple

Sometimes you may need to round the value to a multiple given number... For example, suppose a company ships goods in boxes of 18 units. With the ROUND function, you can determine how many crates are required to deliver 204 items. V in this case the answer is 12, because 204 divided by 18 yields 11.333, which needs to be rounded up. The 12th box will contain only 6 items.

May also need to be rounded negative meaning up to a multiple of negative or fractional - up to a multiple of a fraction. To do this, you can also use the function Okruglt.

In approximate calculations, it is often necessary to round off some numbers, both approximate and exact, that is, remove one or more final digits. There are some rules to follow to ensure that an individual rounded number is as close as possible to the number being rounded.

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, it is increased by one. Strengthening is also assumed when the first of the removed digits is 5, and after it there is one or some significant digits.

The number 25.863 is rounded off as 25.9. In this case, the digit 8 will be amplified to 9, since the first cutout digit 6 is greater than 5.

The number 45.254 is rounded off as - 45.3. Here, the 2 will be amplified to 3, since the first clipping digit is 5, followed by the significant 1.

If the first of the cut-off digits is less than 5, then amplification is not performed.

The number 46.48 is rounded off as - 46. 46 is closer to the number to be 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 amplified if it is odd.

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

The number 0.935 is rounded off as - 0.94. The last digit 3 to be left is amplified as it is odd.

Rounding numbers

Numbers are rounded up when complete precision is unnecessary or impossible.

Round off the number to a certain digit (sign), then replace it with a number close in value with zeros at the end.

Natural numbers are rounded to tens, hundreds, thousands, etc. Digit names in digits natural number you can recall natural numbers in the topic.

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

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

If the number is rounded up to hundreds, then the digit zero must be in both the ones and tens places.

The number obtained by rounding off is called the approximate value of this number.

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

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

Underline the digit of the digit to which the number should be rounded.
Separate all digits to the right of this digit with a vertical bar.
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. The digit of the category to which we rounded off is left unchanged.
If the digit 5, 6, 7, 8 or 9 is 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 digit of the digit to which they were rounded.

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

After the underlined number there is the number 8, which means that we add 1 to the number of the thousand place (we have it 7), and replace all the numbers separated by a vertical line with zeros.

Now let's round 756,485 to hundreds.

Let's round 364 to tens.

3 6 | 4 ≈ 360 - it costs 4 in the ones place, so we leave 6 in the tens place unchanged.

On the number axis, the number 364 is enclosed between the two "round" numbers 360 and 370. These two numbers are called approximate values of 364 with an accuracy of tens.

Number 360 - approximate downside value, and the number 370 is an approximate excess value.

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

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

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

Rounding is also used to roughly check the answer in calculations.

Before an accurate calculation, let's make an estimate of the answer, rounding the multipliers 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 perform an estimate by rounding and dividing numbers.

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

Rounding rules

What is rounding? This is to drop a few digits that are the last in the exact number row. So, following our example, we dropped all the last digits to get an integer (3) and dropped the digits, leaving only the tens (3.3) places. The number can be rounded to hundredths and thousandths, ten thousandths and other numbers. It all depends on how accurate the number is to get. For example, in the manufacture of medicines, the amount 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 what the performance of students in school is, then most often a number with a decimal or with a hundredth place is used.

Consider another example that uses rounding rules. For example, there is a number 3.583333, which needs to be rounded to thousandths - after rounding, we should have three digits behind the decimal point, that is, the result will be the number 3.583. If this number is rounded to tenths, then we get not 3.5, but 3.6, because after the “5” there is the number “8”, which is already equal to “10” during rounding. Thus, following the rules for 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 stored remains unchanged. Such rules for rounding numbers apply regardless of whether to an integer or to tens, hundredths, etc. you need to round off the number.

In most cases, when you need to round a number with the last digit "5", this process is not performed correctly. But there is also such a rounding rule that applies to just such cases. Let's look at an example. Round the number 3.25 to tenths. Applying the rules for rounding numbers, we get the result 3.2. That is, if there is no digit after "five" or there is zero, then the last digit remains unchanged, but only on condition that it is even - in our case, "2" is an even digit. If we were to round up 3.35, the result would be 3.4. Since, in accordance with the rounding rules, if there is an odd digit before "5" that must be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after "5". In many cases, simplified rules can be applied, according to which, if there are digit values from 0 to 4 behind the last stored digit, 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 the number to a certain digit, we underline the digit of this digit, and then replace all the digits behind the underlined one with zeros, and if they are after the decimal point, we discard it. If the first zero-replaced or dropped digit is 0, 1, 2, 3, or 4, then the underlined number leave unchanged... If the first zero-replaced or dropped digit is 5, 6, 7, 8 or 9, then the underlined number increase by 1.

Examples.

Round up to integers:

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

Solution. We underline the number in the category of units (whole) 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 the underlined number will be increased 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 tenths:

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

Solution. We underline the number in the tenth place, and then we act according to the rule: we discard everything after the underlined number. If the underlined digit was followed by the digit 0 or 1 or 2 or 3 or 4, then the underlined digit is not changed. 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. There is a six behind the nine, therefore, we increase the nine by 1. (9 + 1 = 10) write zero, 1 goes to the next digit and it will be 19. It's just that we can't write 19 in the answer, since it should be clear that we were rounding to tenths - the number in the tenth place should be. Therefore, the answer is 19.0.

Round to hundredths:

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

Solution. We underline the digit in the hundredth place and, depending on which digit is 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: in the answer of the latter there should be a digit in the place to which you rounded.

www.mathematics-repetition.com

How to round a number to an integer

Applying the rule for rounding numbers, let's look at specific examples of how to round a number to an integer.

The rule for rounding a number to an integer

To round a number to an integer (or round a number to one), you need to drop the comma and all numbers after the comma.

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

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

Round up a number to an integer:

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

Rounding off the number to the nearest whole, discard the comma and all the following numbers. Since the first of the discarded digits is 8, we increase the previous one by one. They read: "Two hundred seventy-four point eight hundred thirty-nine thousandths is approximately equal to two hundred seventy-five points."

When rounding a number to an integer, discard all the numbers behind 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 whole."

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

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 points." And a couple more examples for rounding a number to integers:

27 Comments

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

Dear ShS! Perhaps (?), In banks rounding takes place according to different rules. I don’t know, I don’t work in a bank. This site deals with the rules in force in mathematics.

how to round the number 6.9?

To round a number to an integer, discard all 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 points.

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

H'm. In this case, financial institutions in matters of rounding are guided not by the laws of mathematics, but by their own considerations.

Tell me how to round 46.466667. Got confused

If you want 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 don't 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 performed to the nearest even number, i.e. the last stored digit is left unchanged if it is even, and amplified if it is odd.

And accordingly: Rounding the number 0.0465 to the third decimal place, we write 0.046. We do not amplify, since the last stored digit 6 is even. The number 0.046 is as close to the given number as 0.047.

Dear Guest! Let it be known to you, in mathematics there are different rounding methods for rounding a number. At school, one of them is studied, which consists in discarding the lower digits of a number. I am glad for you that you know another way, but it would be nice not to forget school knowledge.

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

how to round off 5499.8 correctly?

If we are talking about rounding to the nearest integer, then discard all digits after the decimal point. The discarded figure is 8, therefore, we increase the previous one by one. This means that 5499.8 is approximately 5500 integers.

Good day!
But this question arose seias:
There are three numbers: 60.56% 11.73% and 27.71% How to round up to whole values? So that a total of 100 remains. If you just round up, then 61 + 12 + 28 = 101 There is a discrepancy. (If, as they wrote, according to the "banking" method - in this case it will work, but in the case, for example, 60.5% and 39.5%, it will turn out to be something else again - we will lose 1%). How to be?

O! helped by the method from "guest 07/02/2015 12:11"
Thanks to"

I don’t know I was taught at school like this:
1.5 => 1
1.6 => 2
1.51 => 2
1.51 => 1.6

Perhaps you were taught that way.

0, 855 to hundredths please help

0, 855≈0.86 (5 dropped, the previous figure is increased by 1).

Round 2,465 to an integer

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

How to round 2.4456 to the nearest integer?

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

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

No. If you want to round 1.45 to the nearest integer, discard the first decimal place. Since it is 4, we do not change the previous digit. Thus, 1.45≈1.

Let's look at examples of how to round to tenths of a number using the rounding rules.

The rule for rounding numbers to tenths.

To round a decimal fraction to tenths, you need to leave only one digit after the decimal point, and discard all the other digits following 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 tenths:

To round the number to tenths, leave the first digit after the decimal point, and discard the rest. Since the first discarded digit is 5, we increase the previous digit by one. They read: "Twenty-three point seventy-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, discard the rest. The first discarded digit is 1, so we don't change the previous digit. They read: "Three hundred forty-eight point thirty-one hundredth is approximately equal to three hundred forty-one point three."

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

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

And a couple more examples for rounding to tenths:

Fractional numbers in Excel spreadsheets can be displayed to varying degrees precision:

most simple method - on the tab “ home"Press the buttons" Increase bit depth" or " Reduce bit depth»;
click right click by cell, in the menu that opens, select “ Cell format ...", Then the tab" Number", Select the format" Numerical", We define how many decimal places there will be after the decimal point (2 decimal places are suggested by default);
click the cell, on the tab " home"Choose" Numerical", Or go to" Other number formats ..."And set it up there.

Here's what the fraction 0.129 looks like if you change the number of decimal places in the cell format:

Please note that A1, A2, A3 contain the same meaning, only the presentation form changes. In further calculations, not the value visible on the screen will be used, but original... For a novice spreadsheet user, this can be a little confusing. To actually change the value, you need to use special functions, there are several of them in Excel.

Rounding formula

One of the commonly used rounding functions is ROUND... It works according to standard mathematical rules. Select the cell, click the icon " Insert function", Category" Mathematical", We find ROUND

We define the arguments, there are two of them - itself fraction and number discharges. We click " OK"And see what happened.

For example, the expression = ROUND (0.129,1) will give a result of 0.1. Zero number of digits allows you to get rid of the fractional part. Choosing a negative number of digits allows you to round the whole part to tens, hundreds, and so on. For example, the expression = ROUND (5.129; -1) will give 10.

Round up or down

Excel provides other tools for working with decimal fractions. One of them - ROUNDUP, gives out the most close number, more modulo. For example, = ROUNDUP (-10,2,0) will give -11. The number of digits here is 0, which means we get an integer value. Nearest whole, greater in absolute value - just -11. Usage example:

ROUNDDOWN is similar to the previous function, but returns the closest value, less in absolute value. The difference in the work of the above tools can be seen from examples:

= ROUND (7,384,0)	7
= ROUNDUP (7,384,0)	8
= ROUNDDOWN (7,384,0)	7
= ROUND (7,384,1)	7,4
= ROUNDUP (7.384,1)	7,4
= ROUNDDOWN (7.384,1)	7,3

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 objects in other situations. Then the given number should be reduced to a certain place, for example, to an integer or to a number with a decimal place. If we bring 3.3333333333… ..3 to an integer, then we get 3, and converting 3.3333333333… ..3 to a number with a decimal place, we get 3.3.