From what date it is rounded up. Rounding numbers

The numbers that we have to deal with in real life are of two types. Some accurately convey the true value, others only approximate. The first call accurate, the second - close.

In real life, approximate numbers are most often used instead of exact ones, since the latter are usually not required. For example, approximate values ​​are used when specifying quantities such as length or weight. In many cases, the exact number cannot be found.

Rounding rules

To get an approximate value, the number obtained as a result of any actions must be rounded, that is, replaced with the nearest round number.

Numbers are always rounded to a certain place. Natural numbers are rounded to tens, hundreds, thousands, etc. When numbers are rounded to tens, they are replaced with round numbers consisting only of whole tens, such numbers have zeros in the ones place. When rounding to hundreds, numbers are replaced by more round ones, consisting only of whole hundreds, that is, zeros are already in the one and the tens place. Etc.

Decimal fractions can be rounded in the same way as natural numbers, that is, to tens, hundreds, etc. But they can also be rounded to tenths, hundredths, thousandths, etc. When rounding decimal places, the digits are not filled with zeros, but are simply discarded. In both cases, rounding is performed according to a certain rule:

If the discarded digit is greater than or equal to 5, then the previous one must be increased by one, and if it is less than 5, then the previous digit does not change.

Let's look at some examples of rounding numbers:

• Round off 43152 to thousands. Here it is necessary to discard 152 units, since the number 1 is to the right of the thousand place, then we leave the previous figure unchanged. An approximate value of 43152, rounded to the nearest thousand, will be 43000.
• Round 43152 to hundreds. The first of the discarded numbers is 5, which means we increase the previous digit by one: 43152 ≈ 43200.
• Round 43152 to tens: 43152 ≈ 43150.
• Round 17.7438 to units: 17.7438 ≈ 18.
• Round off 17.7438 to tenths: 17.7438 ≈ 17.7.
• Round 17.7438 to hundredths: 17.7438 ≈ 17.74.
• Round off 17.7438 to thousandths: 17.7438 ≈ 17.744.

The ≈ sign is called the approximate equal sign, it reads - "approximately equal".

If, when rounding the number, the result is greater than the initial value, then the resulting value is called approximate value with excess if less - approximate value with a deficiency:

7928 ≈ 8000, number 8000 - approximate value with excess
5102 ≈ 5000, number 5000 is an approximate value with a drawback

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 determine how many decimal places there will be after the decimal point (2 decimal places are offered by default);
• we 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 initial... 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 the closest 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:

To consider the feature of rounding a number, it is necessary to analyze specific examples and some basic information.

How to round numbers to the nearest hundredth

• To round a number to hundredths, you must leave two digits after the decimal point, the rest, of course, are discarded. If the first digit to be discarded is 0, 1, 2, 3, or 4, then the previous digit remains unchanged.
• If the discarded digit is 5, 6, 7, 8 or 9, then you need to increase the previous digit by one.
• For example, if you need to round off the number 75.748, then after rounding we get 75.75. If we have 19.912, then as a result of rounding, or rather, in the absence of the need to use it, we get 19.91. In the case of 19.912, the digit after the hundredths is not rounded, so it is simply discarded.
• If we are talking about the number 18.4893, then rounding to hundredths is as follows: the first digit to be discarded is 3, so no changes are made. It turns out 18.48.
• In the case of the number 0.2254, we have the first digit, which is discarded when rounded to hundredths. This is a five, which indicates that the previous number needs to be increased by one. That is, we get 0.23.
• There are also times when rounding changes all digits in a number. For example, to round to the nearest hundredth the number 64.9972, we see that the number 7 rounds the previous ones. We get 65.00.

How to round numbers to integers

The situation is the same when rounding numbers to integers. If we have, for example, 25.5, then after rounding we get 26. In the case of a sufficient number of digits after the decimal point, rounding occurs as follows: after rounding 4.371251, we get 4.

Rounding to tenths is done in the same way as in the case of hundredths. For example, if you need to round up the number 45.21618, then we get 45.2. If the second digit after the tenth is 5 or more, then the previous digit is increased by one. As an example, round off 13.6734 to get 13.7.

It is important to pay attention to the number that is located in front of the one that is cut off. For example, if we have the number 1.450, then after rounding we get 1.4. However, in the case of 4.851, it is advisable to round up to 4.9, since there is still one after the five.

Suppose 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 provides general guidelines to consider when rounding numbers to a specified number of significant digits. You can experiment with the rounding functions and substitute your own numbers and parameters to get a number with the desired number of significant digits.

Negative numbers to be rounded are first 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 a value to a multiple of a specified number. For example, suppose a company delivers goods in boxes of 18 units. With the ROUND function, you can determine how many crates are required to deliver 204 items. In this case, the answer is 12, since 204 divided by 18 yields 11.333, which needs to be rounded up. The 12th box will contain only 6 items.

You may also need to round a negative value to a multiple of a negative or a fraction to a multiple of a fraction. To do this, you can also use the function OKRUGLT.

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, 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 the discarding of 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 where rounding rules are applied. 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" is the number "8", which is already equal to "10" during rounding. Thus, following the rules for rounding numbers, you need to know 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, if you need to round a number with the last digit "5", this process is not performed correctly. But there is also a rounding rule that applies to just such cases. Let's look at an example. Round 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.