From what date is rounded into the biggest. Rounding numbers

The numbers with which we have to deal in real life are two types. Some exactly transmit the true size, others - only approximate. The first call accurate, second - approximated.

In real life, most often use approximate numbers instead of accurate, since the latter are usually not required. For example, approximated values \u200b\u200bare used when specifying such values \u200b\u200bas a length or weight. In many same cases, it is impossible to find the exact number.

Rules of rounding

To obtain an approximate value obtained as a result of any actions, the number needs to be rounded, that is, replace it with the nearest round number.

The numbers are always rounded to a certain discharge. Natural numbers are rounded up to dozen, hundreds, thousands, etc. When rounding the numbers to dozen, they are replaced by round numbers consisting only of whole dozens, in such numbers in the discharge of units are zeros. When rounding to hundreds, the numbers are replaced with more round, consisting of only hundreds, that is, zeros are already in the discharge of units, and in the discharge of dozens. Etc.

Decimal fractions can be rounded as well as natural numbers, that is, up to dozen, hundreds, etc. But they can also be rounded to tenths, hundredths, thousandth parts, etc. When rounding decimal places, the discharge is not filled with zeros, but Just discarded. In both cases, rounding is made according to a specific rule:

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

Consider several examples of rounding numbers:

• Round 43152 to thousands. Here it is necessary to discard 152 units, since the digit 1 is worth the right of thousands of thousands, then the previous number retains unchanged. The approximate value of Number 43152, rounded to thousands will be 43000.
• Round 43152 to hundreds. The first of the discarded numbers 5, so the previous figure is increasing by one: 43152 ≈ 43200.
• Round 43152 to tens: 43152 ≈ 43150.
• Round out 17.7438 to units: 17,7438 ≈ 18.
• Round out 17.7438 to the tenths: 17,7438 ≈ 17.7.
• Round out 17.7438 to hundredths: 17,7438 ≈ 17.74.
• Round out 17,7438 to thousandths: 17,7438 ≈ 17,744.

The sign is called the sign of approximate equality, it is read - "approximately equal."

If the number when rounding the number it turned out more initial value, then the value obtained is called approximate extension valueif less - approximate value with disadvantage:

7928 ≈ 8000, the number 8000 is an approximate extension value
5102 ≈ 5000, the number 5000 is an approximate value with a disadvantage

Fractional numbers in Excel spreadsheets can be displayed with varying degrees. accuracy:

• most plain Method - on the tab " the main»Press the buttons" Increase bit" or " Reduce bit»;
• click right mouse button By cell, in the open menu, choose " Format cells ...", Then tab" Number", Choose the format" Numerical"I define how many decimal places after the comma (by default 2 characters are offered);
• click the cell on the tab " the main»Choose" Numerical", Either go to" Other numeric formats ..."And there are set up there.

This is how the fraction of 0.129 looks like, if you change the amount of decimal places after the semicolon in the cell format:

Note, in A1, A2, A3 is recorded the same value, only the form of representation is changing. In further calculations, it will be used not the magnitude apparent on the screen, but source. The novice user of the spreadsheet can be slightly confused. To really change the value, you need to use special functions, there are several in Excel.

Formula rounding

One of the frequently used rounding functions - District. It works according to standard mathematical rules. We choose the cell, click the icon " Insert a function", Category" Mathematical", Find District

Determine the arguments, their two - herself fraction and quantity discharges. Click " OK"And we look at what happened.

For example, expression \u003d Rounded (0.129; 1) Give the result 0.1. The zero number of discharges allows you to get rid of the fractional part. The choice of a negative number of discharges allows you to round the whole part up to dozen, hundreds and so on. For example, expression \u003d Rounded (5,129; -1) Dast 10.

Round in big or smaller

Excel presents other means to work with decimal fractions. One of them - District, gives the closest number more By module. For example, expression \u003d rounded (-10.2; 0) will give -11. The number of discharges here 0, which means that we get an integer value. NearestMore than module, - just -11. Example of use:

Districtlnoon Similar to the previous function, but gives the nearest value less than the module. The difference in the work of the following means is seen from examples:

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

How to round numbers to hundredths

• To round the number to the cells, it is necessary to leave the two digits after the comma, the rest, of course, are discarded. If the first figure, which is discarded, is 0, 1, 2, 3 or 4, the previous digit remains unchanged.
• If the discarded digit is 5, 6, 7, 8, or 9, then you need to increase the previous number per unit.
• For example, if you need to round 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 for its use, we get 19.91. In the case of 19.912, the figure that comes after the hundredths is not rounded, so it is simply discarded.
• If we are talking about number 18,4893, then rounding to the cells is as follows: the first figure that needs to be discarded is 3, so no changes occur. It turns out 18.48.
• In the case of a number of 0.2254, we have the first digit that is discarded when rounding to the 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 cases when rounding changes all the numbers among the number. For example, to round up to the cells number 64.9972, we see that the number 7 is rounded the previous one. We get 65.00.

How to round numbers to whole

When rounding the numbers to the whole situation is the same. If we have, for example, 25.5, then after rounding we get 26. In the case of a sufficient number of digits after a comma, rounding occurs in this way: after rounding 4,371251 we obtain 4.

The rounding to the tenths occurs in the same way as in the case of hundreds. For example, if you need to round the number 45.21618, then we get 45.2. If the second digit after the tenth is 5 or more, the previous digit increases by one. As an example, 13,6734 can be rounded, and in the end it turns out 13.7.

It is important to pay attention to the figure that is located in front of the one that is cut off. For example, if we have the number of 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 after the five there is still a unit.

Suppose you want to round the number to the nearest whole, since the decimal values \u200b\u200bare not important to you, or submit a number in the form of degree 10 to simplify approximate calculations. There are several ways rounding numbers.

Changing the number of semicolons without changing the value

On Sheet

In the built-in numerical format

Rounding number up

Rounding number to the nearest value

Rounding the number to the nearest fractional value

Rounding the number to the specified number of significant discharges

Significant discharges are discharges that affect the accuracy of the number.

The examples of this section use functions. District, District and Districtlnoon. They show ways rounding positive, negative, integers and fractional numbers, but the above examples cover only a small part of the possible situations.

The list below contains general rules that need to be considered when rounding the numbers to the specified number of significant discharges. You can experiment with rounding functions and substitute your own numbers and parameters to get a number with the desired number of significant discharges.

The rounded negative numbers are primarily converted into absolute values \u200b\u200b(values \u200b\u200bwithout a "minus" sign). After rounding, the minus sign is reused. Although it may seem illogical, this is how rounding is done. For example, when using the function Districtlnoon For rounding the number -889 to two significant discharges, the result is the number -880. First -889 is converted to absolute value (889). Then this value is rounded up to two significant discharges (880). After that, the "minus" sign re-applies, which results in -880.

When applied to a positive number of functions Districtlnoon It is always rounded down, and when applying the function District - up.

Function District Rounds fractional numbers as follows: If the fractional part is greater than or equal to 0.5, the number is rounded upwards. If the fractional part is less than 0.5, the number is rounded down.

Function District Rounds integers up or down in the same way, while instead of divider 0.5 used 5.

In general, when rounding the number without a fractional part (integer), it is necessary to subtract the length of the number from the desired number of significant discharges. For example, to round up 2345678 down to 3 significant discharges, a function is used. Districtlnoon with parameter -4: \u003d Rounded) (2345678, -4). At the same time, the number is rounded to a value of 2340000, where part "234" represents significant discharges.

Rounding the number to a given multiple

Sometimes it may be necessary to round the value to a multiple of the specified number. For example, let's say that the company supplies goods in boxes of 18 units. Using the roundt function, you can determine how many boxes will be required to supply 204 units of goods. In this case, the answer is 12, since the number 204 during division to 18 gives a value of 11.333, which must be rounded upwards. In the 12th drawer there will be only 6 units of goods.

It may also be necessary to round the negative value to the multiple negative or fractional - to a multiple fractional. To do this, you can also apply the function District.

In some cases, the exact number in dividing a certain amount to a specific number cannot be determined in principle. For example, when dividing 10 to 3, we turn out 3,3333333333 ... ..3, that is, this number cannot be used to count specific items and in other situations. Then this number should lead to a certain discharge, for example, to an integer or to a number with a decimal discharge. If we give 3.33333333333 ... ..3 to an integer, then we get 3, and leading 3,3333333333 ... ..3 to a number with a decimal discharge, we get 3.3.

Rules of rounding

What is rounding? This discarding several digits that are the last in a number of exact numbers. So, following our example, we dropped all the last figures to get an integer (3) and dropped the numbers, leaving only tens (3.3) discharges. The number can be rounded to hundredths and thousandth, ten-thousand and other numbers. It all depends on how exactly the exact number must be obtained. For example, in the manufacture of medicines, the amount of each of the ingredients of the drug is taken with the greatest accuracy, since even a thousandth gram can lead to a fatal outcome. If you need to calculate, what the performance of students in school, then the number with a decimal or a hundredth discharge is most often used.

Consider a different example in which rounding rules apply. For example, there is a number of 3,583333, which must be rounded up to thousands - after rounding, for the comma, we should remain three digits, that is, the result will be the number 3,583. If this number is rounded to the tenths, then we will succeed in 3,5, and 3.6, since after "5" there is a number "8", which is already equivalent to "10" during rounding. Thus, following the rules of rounding numbers, it is necessary to know if the numbers are greater than "5", then the last figure that needs to be kept will be increased by 1. If there is a figure, less than "5", the last saved digit remains unchanged. Such rules rounding numbers are applied regardless of whether to an integer or up to dozen hundredths, etc. It is necessary to round the number.

In most cases, if necessary, rounding the number in which the last digit "5" is incorrectly performed. But there is also such a rounding rule, which concerns exactly such cases. Consider on the example. It is necessary to round the number 3.25 to the tenths. Applying the rules of rounding numbers, we obtain the result of 3.2. That is, if after "five" no digit or worth zero, then the last figure remains unchanged, but only if it is even - in our case, "2" is an even figure. If we needed rounding 3.35, then the result was the number 3.4. Since, in accordance with the rules of rounding, in the presence of odd figures before "5", which must be removed, an odd figure increases by 1. But only if there are no significant digits after "5". In many cases, simplified rules can be applied according to which, if there is a digit value from 0 to 4, the saved digit is not changed. If there are other numbers, the latter digit increases by 1.