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Rounding numbers up to 2 decimal places. Rounding in Excel - Step-by-step instructions

Program Microsoft Excel. It works, among other things, with numeric data. When performing division or work with fractional numbers, the program produces rounding. This is due, first of all, with the fact that absolutely accurate fractional numbers are rare when necessary, but it is not very convenient to operate with a bulky expression with several signs after the comma. In addition, there are numbers that in principle are not accurately rounded. But at the same time, an insufficiently accurate rounding can lead to rough errors in situations where preciseness is required. Fortunately, the Microsoft Excel program has the ability to install the users themselves, how the numbers will be rounded.

All the numbers with which it works microsoft program Excel is divided into accurate and approximate. The memory is stored in memory of up to 15 discharge, and displayed before the discharge, which will indicate the user itself. But, at the same time, all calculations are performed according to stored in memory, and not displayed on the data monitor.

Using rounding operation, Microsoft Excel throws some number of semicolons. In Excel, a generally accepted rounding method is used when the number is less than 5 is rounded in a smaller side, and more or equal to 5 - in the most side.

Rounding with buttons on the ribbon

Most. simple way Change the rounding of the number is to select a cell or group of cells, and while in the "Home" tab, click on the tape to the "Enlarge Big" button or "Reduce Bigness". Both buttons are located in the "Number" toolbar. At the same time, only the displayed number will be rounded, but for computations, if necessary, up to 15 digits of numbers will be involved.

When you click on the "Enlarge Bottomy" button, the number of characters made after the comma increases by one.

When you click on the "Reduce Blossomy" button, the number of numbers after the comma decreases to one.

Rounding through cell format

You can also set rounding using the cell format settings. To do this, you need to highlight the range of cells on the sheet, click the right mouse button, and in the menu that appears, select "Format cells".

In the cell format settings window that opens, you need to go to the "Number" tab. If the data format is not specified, then you need to select a numeric format, otherwise you will not be able to adjust the rounding. In the central part of the window near the inscription "The number of decimal signs" simply specify the number of signs that we wish to see when rounding. After that, we perform click on the "OK" button.

Setting accuracy calculations

If in previous cases, the parameters installed only on external display Data, and during calculations, more accurate indicators were used (up to 15 characters), now we will tell you how to change the accuracy of the calculations.

The Excel parameters window opens. In this window, go to subsection "Optional". We are looking for a settings block called "when recalculating this book". Settings in this Boca are applied to any sheet, and the entire book as a whole, that is, to the entire file. We put a tick opposite the parameter "Set accuracy as on the screen". Click on the "OK" button located in the lower left corner of the window.

Now, when calculating the data, the displayed number on the screen will be taken into account, and not the one that is stored in the Excel memory. The setting of the displayed number can be carried out by any of the two methods that we talked above.

Application of functions

If you want to change the rounding value when calculating relatively one or more cells, but do not want to reduce the accuracy of calculations in general for the document, then in this case, it is best to take advantage of the possibilities that the "rounded" function and its various variations, as well as Some other functions.

Among the main functions that regulate rounding should be allocated as follows:

  • Rounded - rounds the specified number of decimal signs, according to the generally accepted rounding rules;
  • Districtlvops - rounds up to the nearest number up the module;
  • Roundlvis - rounds up to the nearest number down the module;
  • DistrictLT - rounds a number with a given accuracy;
  • OKRWP - rounds the number with a given accuracy up the module;
  • Occording - rounds the number down module with a given accuracy;
  • Scroll - rounds the data to an integer;
  • Even - rounds the data to the nearest even number;
  • An odd - rounds the data to the nearest odd number.

For the functions of the rounded, the next input format is the following input format: "The name of the function (number; number of units). That is, if you, for example, you want to round the number of 2.56896 to three digits, then apply the function of the rounded (2,56896; 3). The output is the number of 2.569.

For the functions of the district, OKRWP and the Obrvinis, such a rounding formula is used: "The name of the function (number; accuracy)". For example, to round the number 11 to the nearest number of multiple 2, we introduce the function of the roundt (11; 2). The output is the number 12.

Functions Outbrows, even and default use the following format: "Name of the function (number)". In order to round the number 17 to the nearest even use the function is even (17). We get the number 18.

The function can be entered both in the cell and in the row of functions, after selecting the cell in which it will be. Before each function, you need to sign "\u003d".

There is a somewhat different way to introduce rounding functions. It is especially convenient to use when there is a table with the values \u200b\u200bthat you need to convert into rounded numbers in a separate column.

For this, go to the "Formulas" tab. Clear "mathematical". Further, in the list that opens, choose the desired function, for example, rounded.

After that, the function arguments opens. In the "Number" field, you can enter a number manually, but if we want to automatically round the data of the entire table, then click on the button to the right of the data introduction window.

The argument window of the function is folded. Now you need to click on the upper cell of the column, the data of which we are going rounded. After the value is entered in the window, click on the button to the right of this value.

The function arguments window opens again. In the "Number of Discharges" field, write the bit to which we need to cut the fraction. After that, we click on the "OK" button.

As you can see, the number rounded. In order to round up the same way and all other data of the desired column, we bring the cursor to the lower right corner of the cell with a rounded value, click on left button Mice, and stretch it down to the end of the table.

After that, all values \u200b\u200bin the desired column will be rounded.

As you can see, there are two main ways to round the visible display of the number: using the tape button, and by changing the parameters of the cell format. In addition, you can change the rounding of actually calculated data. It can also be made in two ways: change the settings of the book as a whole, or by applying special functions. The choice of a particular way depends on whether you are going to apply a similar type of rounding for all data in the file, or only for a specific range of cells.

Rounding in Excel, first of all, it is necessary for convenient formatting numbers.

This can be done both to an integer value and up to a certain number of decimal signs.

Round the number to a certain number of semicolons

It is worth noting that it is necessary to round the numbers correctly. It is not enough to simply take and remove several characters after the comma in a long meaning.

Otherwise, the final calculations in the document will not comply.

You can round down using the built-in program functionality. In fact, the figure is updated only visually, and in the cell there remains real value.

Thus, it is possible to calculate without loss of data, while the user will work comfortably with large sums and make the final report.

The figure shows a list of basic functions rounding and the result of their use:

To commit simple procedure rounding numbers to several decimal places (in this case - up to 2 characters), follow the instructions:

  • Open the previously used document or create a new one and fill it with the necessary data;
  • In the Formulas tab, open the drop-down list with mathematical functions and find those that are designed for rounding, as shown in the figure below;

  • Enter the function arguments and fill in all fields of the dialog box, as shown in the figure;

  • The resulting function will be written in the box for the cell formulas. To apply it to all the other cells, copy it.

Rounding to an integer

In order to round the decimal number to the whole, you can use several functions at once, namely:

  • OKRWP - Using this featureYou can round up to an integer value in the whole.
  • District - rounds the selected number on all canons of mathematical rules;
  • Okrvin - This is a function that is intended for rounding decimal to an integer value at a smaller side of the whole.
  • Otbr. - the function drops all the numbers after the comma, leaving only an integer value;
  • Current - rounding to an integer value until it turns out even;
  • Odd - the function is opposite to even;
  • District - rounding with the accuracy that the user itself will indicate in the program dialog box.

Using the above functions, you can create an integer number according to the user's requirement.

After selecting a function, in the dialog box that opens, specify accuracy equal to zero.

Thus, the decimal signs will not be taken into account.

Rounding to closest multiple

In addition to all rounding options, the exile table can be rounded the values \u200b\u200bto the closest multiple number to it.

This method provides the function of OKRGLKRTN. It is available in the Standard Mathematical Built-in Program Functions section.

In the Function window, enter the coordinate of the cell in which the number is located. In the "Accuracy" field, place the value "1" or other necessary option.

Accuracy is also a multiple to which you need to round the specified number.

At the bottom you can see the value that will be shown in the cell. It can be adjusted directly in the dialog box.

Outcome

Thanks to the detailed consideration of this issue of numbers in the Table Excel processor, you can correctly and quickly resolve all the readings in the document without facing errors in the final calculations after rounding.

Rounding numbers in Excel

Video tutorial about the various possibilities rounding numbers in Excel.

Question: How to round the numbers in Excel, are interested in many users. We will talk about him about him.

You can round the numbers in Excel in several ways: using cell format, or using a rounding formula. These two ways should be distinguished. The use of the format of the rounding cells is more suitable if you just need to display values \u200b\u200bin a cell or display data to print. Formulas allow you to select the desired rounding for a number in the cell so that it can be used for other calculations.

Rounding numbers can be produced in a large or smaller side, to specified number decimal discharges, up to dozen, hundreds and so on. You can round up to an even or odd number, or to discard all the numbers after the comma at all.

Rounding the number using cell format

The format of the cells will allow you to choose the required number of numbers, which should be displayed in the number after the comma.

We will round the number 23,5168 in the A1 cell. I click on it with right mouse button and select "cell format" from the context menu.

The number of decimal signs has decreased to 2. As you can see, rounding the number occurs in mathematical laws: if the discarded number is less than five - the number is rounded in a smaller side, if more than five or equal - to the greater.

The value in the cell changed only visually. The formula string still costs the number 23,5168, and it is it that will be taken for any calculations in which the A1 cell will be indicated.

To reduce or increase the number of semicolons, you can use the following method. On the Home tab in the "Number" group you will find two buttons "Enlarge Bigness" and "Reduce the bit".

Highlight the A1 cell and press once on the button. "Reduce the bit". We get this result.


Functions for rounding in Excel

Rounding the number in the cell using special functions will allow it to be used to calculate the formulas.

The functions required for calculations are located on the Formula tab in the section "Mathematical". Consider what makes each of them.

Select C1 cell and call the desired function.

Rounded - round number to specified number decimal discharges. In the "Number" field - specify the address of the desired cell, in the field "Number of discharges" - Specify the number of semicolons. If you write "0", the rounding will occur until an integer.


The formula string will be written as follows: \u003d rounded (A1; 3). A1 - reference to the cell; 3 - the number of decimal discharges.

Rounded the number in Excel can be up to dozen, hundreds, thousands. To do this in the field "Number of discharges" need to write -1; -2; -3, respectively.

Districtlvops - round the number in the biggest, that is, rounds the value to the nearest more. Record :.


Roundalvina - rounds in a smaller side, that is, to the nearest fewer. Recording: \u003d Rounded line (number; number of discharges).


To round in Excel up to an integerYou can use any of the above functions. In this case, in the field "Number of discharges" You need to write "0". Or specify a given number in the formula row.


The whole - will allow you to round the value to the nearest smaller. Recording: \u003d whole (number).


To round the number to the nearest larger whole, use rounding to dozen using the Roundlock function. Recording: \u003d Rounded (number; number of discharges).


Unclear - rounds the value to the nearest accurate odd number. Moreover, if the value in the cell is positive - in the most side, negative - to a smaller one. Recording: \u003d Net (Number).


Current - rounds the value to the nearest integer even number. Record: \u003d even (number).


Otbr - will allow to discard the fractional part, leaving an integer. According to the laws of mathematics, 23,5168 was to be rounded up to 24, and we have a number 23 - the fractional part is simply discarded. Recording: \u003d OTBR (number; number of discharges).


District Through the number with a given accuracy. If you put "7" in the "Accuracy" field, the number 23,5168 is rounded to the nearest number, which is multiple of seven. Recording: \u003d Rounded (number; accuracy).


Using methods and various formulas described in this article, you will be able to round the number in Excel as it is necessary in the document: with a certain amount of decimal discharges, to a large or smaller side, to a whole, up to a tet and thousand.

When working with tables, it is often necessary to round the number in Excel, for this there is a number of existing mathematical functions. But it is necessary to understand the difference between rounding and formatting the cell value. Consider all the nuances more ...

Formatting, number of semicolons

Any numeric value entered into the cell is displayed in the "General" format (main menu or cell format). In the case of formatting a number, it displays a certain number of semicolons that can be configured (, cell format). Those. You can specify any number of semicolons with formatting.

Rounding Functions Rounded (), District Top (), rounded

When values \u200b\u200bare used by formulas, the program works with its actual value that may differ from what we see on the monitor (for example, in cells B1 of the first picture). The rounding of the number occurs with the features (formulas) of the rounded area (), rounded (), rounded, rounded.

DistrictLT (128; 6) to round the number "127" to a multiple "6" in the formula row must be prescribed: \u003d rounded (128; 6), in the final cell we get the number "126".

Rounding monetary values

Very often, counting money in Excel, in which additional calculations are used, we get a number with a large number of semicolons. Monetary formats provide for only two decimal signs, so the value must be brought to the proper form, roundate the number in Excel.

For this, if the cell B1 contains a numeric figure of 10.561 p. (This format can be set by pressing the icon with money in the second picture) to bring the value to the desired (2 decimal sign) sufficient in the formula row to protrure: \u003d rounded (B1; 2), we obtain the result of 10.56 p.

There are cases that the value must be rounded in a large or smaller side, for this, formulas are used:

1. rounding to the biggest, i.e. Up: \u003d OKRWP (B1; 0.01), cell B1 will receive a value of 10.57 p., with rounding to the next penny (0.01) to the biggest side
2. Rounding in a smaller side, down: \u003d Occording (B1; 0.01), the cell will receive a value of 10.56 p., With rounding to the next penny to the smaller side
3. And if for example, round up an indicator of up to 10 kopecks Use the formula: \u003d OKRWP (B2; 0.10)

Converting an integer

In order to obtain an integer in Excel, formulas \u003d integer () and \u003d sampl (). At first glance, they may seem like, but it is not, it is especially clearly visible on negative numbers. When using a formula with a function, only the fractional part of the number is removed.

For example, we have a number-16.3543, formula: \u003d Otbr (-16,3543) converts the value to the number -16, and the formula: \u003d the whole (-16,3543) gives an indicator -17, because, the whole next number goes For "-16,3543" - it is "-17".

Sometimes the sampling function is used, for the truncation of decimal signs of the formula: \u003d Otbr (16,3555555; 2) gives the indicator "16.35".

How to round the number in Excel up or down

It happens that large digital values \u200b\u200bmust be rounded up to a certain number of some significant digits up or down. To do this, we use formulas with the OPCWP function and the Ocline. For example, we have a number 164 358 in cells B1, formula: \u003d rounded (B2; 3-DLSTR (B1)), converts it to the "165000" indicator, the top three in this formula is just a value that is responsible for the number of characters in the conversion. If we replace it for example on "2" and write a formula \u003d rounded (B2; 2-dlster (A1)), we get the value "160,000".

It should be noted that all these formulas work only with positive numbers.

Banking rounding

Very often in accounts, such as 1C is used by a bank rounding, which says Wikipedia: Banking rounding (Banker's Rounding) or accounting rounding - rounding here occurs to the nearest even (if the number ends at 5), that is, 2.5 → 2, 3.5 → 4. To do this, you can use the following functions:

Rounding to even / odd

Function \u003d even () rounds to the nearest even whole. At the same time, positive numbers are rounded upwards, and negative - to a decrease

Function \u003d nothing () rounds the number to the nearest odd whole. Positive numbers are rounded in the direction of magnification, and negative - to a decrease

Rounded the numbers in Excel in several ways. Using cell format and using functions. These two methods should be distinguished as follows: the first only to display the values \u200b\u200bor output to print, and the second method also for calculations and calculations.

Using functions, it is possible to accurate rounding, in a large or smaller side, to a user-defined discharge. And the values \u200b\u200bobtained as a result of calculations can be used in other formulas and functions. At the same time, rounding using the cell format will not give the desired result, and the results of calculations with such values \u200b\u200bwill be erroneous. After all, the format of the cells, in fact, the value does not change, only its way of displaying changes. So that you quickly and easily figure out and do not make mistakes, we give a few examples.

How to round the number of cell format

We offer 76,575 in cell A1. By right-clicking, call the "Cell Format" menu. You can do the same through the "Number" tool on the main page of the book. Or press the combination of hot keys Ctrl + 1.

Select a numeric format and set the number of decimal signs - 0.

Rounding result:

You can assign the number of decimal signs in the "monetary" format, "Financial", "percentage".

As can be seen, rounding occurs in mathematical laws. The last figure that needs to be saved is incremented by one if the number follows the number more or equal to "5".

The peculiarity of this option: the greater the numbers after the comma, we will leave, the more accurate the result.

How to round the number in Excel

Using the rounded function () (rounded to the number of decimal discharges necessary to the user). To call "Wizards of Functions" We use the FX button. The desired function is in the "mathematical" category.

Arguments:

  1. "Number" - reference to a cell with the desired value (A1).
  2. "The number of discharges" is the number of decimal signs, to which the number will be rounded (0 - to round up to an integer, 1 - one sign is left after a comma, 2 - two, etc.).

Now rounded an integer (not a decimal fraction). We use the function rounded:

  • the first argument of the function is a link to the cell;
  • the second argument - with the sign "-" (up to dozen - "-1", to hundreds - "-2" to round the number to thousands - "-3", etc.).

How to round the number in Excel to thousands?

An example of rounding the number to thousands:

Formula: \u003d rounded (A3; -3).

You can round up not only the number, but also the expression value.

Suppose there is data on the price and number of goods. It is necessary to find the cost with accuracy to the ruble (rounded to an integer).

The first argument of the function is a numerical expression for finding the cost.

How to round down in the big and smaller side in Excel

For rounding to the large side - the "District Top" function.

The first argument fill in the already familiar principle - reference to the cell with data.

The second argument: "0" - rounding the decimal fraction to the whole part, "1" - the function rounds, leaving one afterpoint sign, etc.

Formula: \u003d rounded (A1; 0).

Result:

To round down at a smaller side in Excel, the "Roundedlice" function applies.

An example of formula: \u003d rounded) (A1; 1).

The result obtained:

Formulas "District Top" and "roundedlice" are used to round the values \u200b\u200bof expressions (works, sums, differences, etc.).

How to round up to an integer in Excel?

To round up to a whole side, use the District Top function. To round up to the whole side, use the "roundliflism" function. The "rounded" function and the format of the cells also allow you to round up to an integer, setting the number of discharges - "0" (see).

The Excel program for rounding to an integer is also applied to the "Otrib" function. She simply discarded the decimal signs. In fact, rounding does not occur. The formula cuts out the numbers to the designated discharge.

Compare:

The second argument "0" - the function cuts off to an integer; "1" - to the tenth lobe; "2" - to the hundredth of the share, etc.

Excel special feature that will return only an integer, "integer. It has a single argument - "Number". You can specify a numeric value or a link to the cell.

The lack of using the "whole" function - rounds only in a smaller side.

It is possible to round up to the integer in Excel using the "OKRWP" and "OKRVNIS" functions. Rounding occurs in a large or smaller side to the nearest integer.

An example of using functions:

The second argument is an indication of the discharge, to which the rounding must occur (10 - up to dozen, 100 - to hundreds, etc.).

The rounding to the nearest whole even performs the function "Cherish", to the nearest odd - "notion".

An example of their use:

Why Excel rounds big numbers?

If in cells tableware processor Large numbers are introduced (for example, 78568435923100756), Excel automatically rounds them as follows: 7,85684E + 16 is a feature of the format of the "General" cells. To avoid this display of large numbers, you need to change the cell format with this large number on the "numeric" (the fastest way to press the Ctrl + Shift + 1 combination of hot keys). Then the cell value will be displayed as follows: 78 568 435 923 100 756.00. If desired, the number of discharges can be reduced: "Home" - "Number" - "Reduce Bigness".

Often the question arises " How to round the number in Excel right, for sure? "In Excel you can round the number exactly or in a large (smaller) side, to an integer, up to dozen, hundreds, etc.
First option.
Rounding to Excel to an integer.
How to remove the numbers after the comma format, see the article "The number of Excel. Format.But there is one catch. If we removed all the numbers after the semicolon, the result may not be correct.For example, there is such a table.
Now we remove the numbers after the comma (cell format). It turned out so.
It turned out: 2 + 3 \u003d 6. It happened, because according to the rules of mathematics, the figure 5 after the comma is rounded into the biggest side.The greater the numbers after the comma, the more accurately believes.
There are two digits after a comma (cell format). It turned out so.
Here we were removed in the column format of the cells of zeros after the comma, and in the final cell left two numbers after the comma. It turned out so.
Second option.
Rounding formula in Excel.
We have such a table.
If we will multiply the price on the quantity, then after the comma will be a few digits.
But with the help of the formula, we can, not only multiply the numbers, but also to immediately round them.In the cell with the sum setthe function "rounded". So, on the Excel tab "Formulas" in the "Library of Functions" section, select "mathematical", clickthe function "rounded".
The "Arguments of Functions" dialog box appeared.Fill it out.
In the "number" line, we write the multiplication formula (quantity prices).
In the line "Number of units" we write 2. This means - 2 decimal sign. Click "OK". It turned out so.

The formula is so. Now copy this formula down dragging. It turned out so.
But, if we still establish a cell format with one digit after a semicolon in this cell, then the number is rounded to one digit after the comma.
In the yellow cell, we installed using the cell format one digit after a comma.
How to write in the "Number of Solids" row.
If we deliver the figure 1, then one digit will stand after the comma.
If we deliver the number 2, then two digits will stand after the comma, etc.
If we deliver 0 - after the comma, there will be no numbers, i.e. will happen rounding to an integer in Excel.
And if you need to round the integer up to dozens, then we put "-1" (minus 1).
For example, the number 123456 needs to round up to hundreds. We put in the line "Number of units" digit -2 (minus 2). It turned out such a number 123500.
How else can be rounded in Excel .
Function "Rounded" – rates a number in Excel according to the rules of mathematics.
Numbers up to 5 rounds in a smaller side. Numbers from 5 to 10 rounded in the biggest.
Function "District Top" – eXCEL rounding in the biggest
For example, rounding up to dozen in Excel produced by such a formula\u003d OKRWP (C12; 10), where the number 10 in the formula means to round up to dozen.
Rounding to hundreds in Excel According to such a formula\u003d OKRWP (C15; 100), etc.
Other rounding methods up to a certain number, etc., see the article "EXCEL Rounding in the biggest."
Function "Roundedlice" – rounding Excel in smaller , leaving after the semicolons as many digits as we point out in the row of the Dialog Dialog box.
Function "OKRWP" – rounding Excel to the whole side up to an integer.

The formula is so. It turned out so. Here the formula number was rounded into the biggest, although according to the rules of mathematics, it is necessary to round down in a smaller direction.
Function "Oblvnis" – rounding Excel to a smaller side up to an integer.
Function "District" – rounds the number of Excel with the accuracy we task. Read more about several ways in the article "Rounding Formula in Excel".
Is there some more rounding functions in Excel:
Function "Court" – rounded the number of Excel as long as it turns out an even number.
The function is "nothing" – rounded the number to the first odd number.
Function "Otbr" – rounds to an integer, throwing all the numbers after the comma.
It happens, you need rounded numbers in Excel to a multiple number. For example, so that all numbers are divided into three without a residue. How to round numbers to a multiple number, see the article "The sum of multiple numbers 3 in Excel".
How to multiply the time to the number (money), for example, hours of work for the cost of one hour, see the article "How to multiply the time to the number in Excel".

It happens that it is necessary to perform rounding in Excel, and users do not know how to do it accurately and right. Meanwhile, the rounding function makes it possible to round the number to a smaller (greater) side to hundreds, tens or an integer. At the same time, there are several ways to do it.

  1. The first way: by using the cell format, remove all the numbers that follow the comma. But in this case, there is a small nuance: if you remove all the zeros after the comma in the existing number of numbers, as well as in the cell with the results, then you can get an incorrect result.
  2. The second way presupposes use of formula. For this, it is necessary to in the cell in which the amount is located, put the function " District": On the formula" tab, choose the "Library of Functions" section, in which we need "mathematical". And already in this section we find and press the desired function "rounded".


After that, a dialog box appears, which is called "functions arguments". You need to fill it. In the number row, you can write the number you are going to round. But you can immediately register any necessary function, for example, multiplication. It will relieve you from extra movements.

Next is the line "Number of Lands", in which you should specify the number of discharges that you need to round the number. So, if you put "3" in this row, then there will remain 3 signs after the comma. At the same time, if you put "0", then the number will automatically round up to the culoge value. If there is a need to round the whole number up to dozen, then for this in the "Solidarizer" string, you should write a negative value. For example, we have a number 123 456, which we want to round up to hundreds. To do this, we put the value "-2" in the graph and get the number 123 500.


Excel has several more functions that will help with rounding. For example,

Rounding the numbers in life accounts for more often than it seems to many. This is especially true for people of those professions related to finance. This procedure people working in this area are well trained. But B. everyday life process bringing values \u200b\u200bto a whole mind Not unusual. Many people were safely forgotten how to round numbers, immediately after school bench. Recall the main points of this action.

In contact with

Round number

Before moving to the rules of rounding values, it is worth understanding what is a round number. If we are talking about integers, it is necessarily ends with zero.

To the question where such skills are useful in everyday life, you can safely answer - with elementary shopping campaigns.

Using the rule of approximate counting, you can estimate how much purchases will cost and what amount must be taken with you.

It is with round numbers it is easier to calculate, without using the calculator.

For example, if in the supermarket or on the market we buy vegetables weighing 2 kg of 750 g, then in a simple conversation with the interlocutor, often does not call the exact weight, but they say that they purchased 3 kg of vegetables. When determining the distance between settlements Also apply the word "about". This means bringing the result to a convenient mind.

It should be noted that with some calculations in mathematics and task solutions, accurate values \u200b\u200bare also not always used. This is especially true in cases where they receive in response infinite periodic fraction. Let us give a few examples when approximate values \u200b\u200bare used:

  • some values \u200b\u200bof permanent values \u200b\u200bare subordinate to the rounded form (the number "PI" and so on);
  • tabletny values \u200b\u200bof sinus, cosine, tangent, catangens, which are rounded to a certain discharge.

Note!As practice shows, the approximation of values \u200b\u200bto the whole, of course, gives an error, but sucks insignificant. The higher the category, the more accurate the result will be.

Receipt of approximate values

This mathematical action is carried out according to certain rules.

But for each number of numbers they are different. It is noted that it is possible to round whole numbers and decimal.

But with ordinary fractions, the action is not performed.

First need them translate to decimal fractionsAnd then proceed to the procedure in the required context.

Rules of approximation of values \u200b\u200bare as follows:

  • for integers - replacement of discharges following rounded, zeros;
  • for decimal fractions - discard all the numbers that are for a rounded discharge.

For example, rounding 303,434 to thousands, it is necessary to replace hundreds, tens and units with zeros, that is, 303,000. In decimal fractions 3,3333 county to tenthx, simply discard all the subsequent numbers and get the result of 3.3.

Accurate rounding rules of numbers

When rounding decimal fractions is not enough enough discard numbers after rounded discharge. You can make sure this is possible on this example. If the store purchased 2 kg of 150 g of sweets, then they say that about 2 kg of sweets are purchased. If the weight is 2 kg of 850 g, then they produce rounding to the most side, that is, about 3 kg. That is, it can be seen that sometimes the rounded discharge is changed. When and how they do, the exact rules will be able to answer:

  1. If, after the rounded discharge it follows the number 0, 1, 2, 3 or 4, then the rounded is left unchanged, and all subsequent numbers are discarded.
  2. If after the rounded discharge it follows the number 5, 6, 7, 8 or 9, then the rounded increases per unit, and all subsequent numbers are also discarded.

For example, how correctly 7.41 closer to units. Determine the figure that follows the discharge. In this case, this is 4. Therefore, according to the rule, the number 7 is left unchanged, and the numbers 4 and 1 are discarded. That is, we get 7.

If the fraction of 7.62 is rounded, then after units it follows the number 6. According to the rule, 7 must be increased by 1, and the numbers 6 and 2 to discard. That is, the result will be 8.

The examples presented are shown how to round decimal fractions to units.

Approach to integers

It is noted that it is possible to round up to units in the same way as well. The principle is the same. Let us dwell more on rounding decimal fractions to a certain discharge in the whole part of the fraction. Imagine an example of approaching 756.247 to dozen. In the discharge of the tenths there is a digit 5. After the rounded discharge it follows the number 6. Consequently, according to the rules it is necessary to perform next steps:

  • rounding in a large side of tens per unit;
  • in the discharge of units, the number 6 is replaced;
  • the numbers in the fractional part of the number are discarded;
  • as a result, 760 are obtained.

Let's pay attention to some values \u200b\u200bin which the process of mathematical rounding to the entire rules does not display an objective picture. If you take a fraction of 8,499, then by converting it according to the rule, we get 8.

But in essence it is not quite so. If it is frozen to round up to whole, then first we get 8.5, and then we discard 5 after the comma, and we carry out rounding to the most side.

We get 9, which, in principle, do not suck exactly. I.e in such values, the error is essential. Therefore, we estimate the task and, if the situation allows, it is better to use a value of 8.5.

Approach to tenths

How to round up to tenths, to hundredths, up to thousands? The operation is carried out according to the same rules as before. The main task is to correctly determine the rounded discharge and the sign that follows it.

For example, fraction 6,7864 when communicating:

  • up to tents becomes equal to 6.8;
  • to the hundredths - 6.79;
  • if rounded to thousands, then receive 6,786.

Note!The ignorance of these rules is very successfully used by marketers. In stores, watching the price tag indicating the number 5.99, the price is perceived by the price equal to 5. In reality, the price of goods is almost 6.

Mathematics - Learning rounding numbers

Rules rounding numbers up to tenths

Output

The priorities of the ability to perform such mathematical operations can be given a lot more. It is important to learn how to correctly assess the situation, set the goal, and the result will come immediately.