You have to round numbers in life more often than many people think. This is especially true for people in those professions that are related to finance. People working in this field are well trained in this procedure. But also in Everyday life process converting values to an integer form Not unusual. Many people have safely forgotten how to round numbers right after school bench. Let us recall the main points of this action.
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round number
Before moving on to the rules for rounding values, it is worth understanding what is a round number. If we are talking about integers, then it necessarily ends with zero.
The question of where such a skill is useful in everyday life can be safely answered - with elementary shopping trips.
Using the rule of thumb, you can estimate how much the purchases will cost and how much you need to take with you.
It is with round numbers that it is easier to perform calculations without using a calculator.
For example, if vegetables weighing 2 kg 750 g are bought in a supermarket or on the market, then in a simple conversation with an interlocutor they often do not give the exact weight, but say that they have purchased 3 kg of vegetables. When determining the distance between settlements, the word "about" is also used. This means bringing the result to a convenient form.
It should be noted that in some calculations in mathematics and problem solving, exact values are also not always used. This is especially true in cases where the response receives endless periodic fraction . Here are some examples where approximate values are used:
- some values of constant quantities are presented in rounded form (number "pi" and so on);
- tabular values of sine, cosine, tangent, cotangent, which are rounded to a certain digit.
Note! As practice shows, the approximation of values to the whole, of course, gives an error, but we suck insignificant. The higher the digit, the more accurate the result will be.
Getting approximate values
This mathematical action is carried out according to certain rules.
But for each set of numbers they are different. Note that integers and decimals can be rounded.
But with ordinary fractions action is not performed.
First they need convert to decimals, and then proceed with the procedure in the required context.
The rules for approximating values are as follows:
- for integers - replacement of digits following the rounded one with zeros;
- for decimal fractions - discarding all numbers that are behind the rounded digit.
For example, when rounding 303,434 to thousands, you need to replace hundreds, tens, and ones with zeros, that is, 303,000. In decimals, 3.3333 rounding up to ten x, just discard all subsequent digits and get the result 3.3.
Precise rules for rounding numbers
When rounding decimals, it's not enough to simply discard digits after rounded digit. You can verify this with this example. If 2 kg 150 g of sweets are bought in a store, then they say that about 2 kg of sweets were purchased. If the weight is 2 kg 850 g, then they are rounded up, that is, about 3 kg. That is, it can be seen that sometimes the rounded digit is changed. When and how this is done, the exact rules will be able to answer:
- If the rounded digit is followed by the digit 0, 1, 2, 3, or 4, then the rounded digit is left unchanged, and all subsequent digits are discarded.
- If the rounded digit is followed by the number 5, 6, 7, 8 or 9, then the rounded one is increased by one, and all subsequent digits are also discarded.
For example, how to properly fraction 7.41 approximate units. Determine the number that follows the discharge. AT this case this is 4. Therefore, according to the rule, the number 7 is left unchanged, and the numbers 4 and 1 are discarded. So we get 7.
If the fraction 7.62 is rounded, then the units are followed by the number 6. According to the rule, 7 must be increased by 1, and the numbers 6 and 2 should be discarded. That is, the result will be 8.
The examples provided show how to round decimals to units.
Approximation to integers
It is noted that you can round to units in the same way as to integers. The principle is the same. Let us dwell in more detail on rounding decimal fractions to a certain digit in the integer part of the fraction. Imagine an example of approximating 756.247 to tens. The number 5 is located in the tenth place. The number 6 follows after the rounded place. Therefore, according to the rules, it is necessary to perform next steps:
- rounding up tens per unit;
- in the discharge of units, the number 6 is replaced;
- digits in the fractional part of the number are discarded;
- the result is 760.
Let's pay attention to some values in which the process of mathematical rounding to integers according to the rules does not reflect an objective picture. If we take the fraction 8.499, then, transforming it according to the rule, we get 8.
But in fact, this is not entirely true. If we round up bit by bit to integers, then we first get 8.5, and then discard the 5 after the decimal point, and round up.
If displaying unnecessary digits causes ###### characters to appear, or if microscopic precision is not needed, change the cell format to display only the required decimal places.
Or if you want to round a number to the nearest major digit, such as a thousandth, hundredth, tenth, or one, use a function in a formula.
With button
Select the cells you want to format.
On the tab home select a team Increase bit depth or Decrease bit depth to display more or less decimal places.
By using built-in number format
On the tab home in a group Number click the arrow next to the list of number formats and choose Other number formats.
In field Number of decimal places enter the number of decimal places you want to display.
Using a function in a formula
Round up to required amount digits using the ROUND function. This function has only 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 round the number to.
Suppose cell A1 contains a number 823,7825 . Here's how to round it up.
Enter =ROUND(A1,-3), which is equal to 100 0
The number 823.7825 is closer to 1000 than it is to 0 (0 is a multiple of 1000)
In this case, a negative number is used because rounding must be to the left of the decimal point. The same number is used in the next two formulas, which are rounded to hundreds and tens.
Enter =ROUND(A1,-2), which is equal to 800
The number 800 is closer to 823.7825 than it is to 900. You probably understand now.
Enter =ROUND(A1,-1), which is equal to 820
Enter =ROUND(A1,0), which is equal to 824
Use zero to round a number to the nearest one.
Enter =ROUND(A1,1), which is equal to 823,8
In this case, use a positive number to round the number to the required number of digits. The same applies to the next two formulas, which are rounded to hundredths and thousandths.
Enter =ROUND(A1,2), which is equal to 823.78
Enter =ROUND(A1,3), which is equal to 823.783
To round to the nearest thousand and
To round to the nearest hundreds
To round up to the nearest dozens
To round up to the nearest units
To round up to the nearest tenths
To round up to the nearest hundredths
To round up to the nearest thousandths
Round a number up with the ROUNDUP function. It works exactly like the ROUND function, except that it always rounds the number up. For example, if you want to round the number 3.2 to zero digits:
=ROUNDUP(3,2,0), which is equal to 4
Round a number down with the ROUNDDOWN function. It works exactly like the ROUND function, except that it always rounds the number down. For example, you need to round the number 3.14159 to three digits:
=ROUNDDOWN(3.14159,3), which is equal to 3.141
Let's say you want to round a number to the nearest whole number because you don't care about decimals, or you want to express a number as a power of 10 to make it easier to approximate. There are several ways to round numbers.
Changing the number of decimal places without changing the value
On the sheet
In built-in number format
Rounding up
Rounding a number to the nearest value
Rounding a number to the nearest fractional value
Rounding a number to the specified number of significant digits
Significant digits are digits that affect the precision of a number.
The examples in this section use the functions ROUND, ROUNDUP and ROUNDDOWN. They show ways to round positive, negative, integer, and fractional numbers, but the examples given cover only a small part of the possible situations.
The list below contains general rules, which must be taken into account when rounding numbers to the 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 number of significant digits you want.
Rounded negative numbers are first converted to absolute values (values without a minus sign). After rounding, the minus sign is reapplied. Although it may seem counterintuitive, this is how rounding works. For example, when using the function ROUNDDOWN to round -889 to two 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 positive number functions ROUNDDOWN it always rounds down, and when applying the function 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 integers 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 need to subtract the length of the number from the right amount significant ranks. For example, to round 2345678 down to 3 significant digits, use the function ROUNDDOWN with -4 option: = ROUNDDOWN(2345678,-4). This rounds the number up to 2340000, where the "234" portion is significant digits.
Rounding a number to a given multiple
Sometimes you may want to round a value to a multiple of a given number. For example, let's say a company ships goods in boxes of 18 units. Using the ROUND function, you can determine how many boxes will be required to deliver 204 items. In this case, the answer is 12 because 204 when divided by 18 is 11.333, which needs to be rounded up. There will be only 6 items in the 12th box.
You may also need to round a negative value to a multiple of a negative value, or a fractional value to a multiple of a fractional value. You can also use the function for this ROUND.
Fractional numbers in Excel spreadsheets can be displayed to varying degrees. accuracy:
- most simple method - on the tab " home» press the buttons « Increase bit depth" or " Decrease bit depth»;
- click right click by cell, in the drop-down menu, select " Cell Format...”, then the tab “ Number", select the format" Numerical”, determine 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 configure 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 have the same meaning, only the form of representation 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 really 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 a cell, click the " Insert function”, category “ Mathematical", we find ROUND 
We define the arguments, there are two of them - herself fraction and amount discharges. We click " OK' and see what happens.
For example, the expression =ROUND(0.129,1) will give a result of 0.1. The zero number of digits allows you to get rid of the fractional part. Choosing a negative number of digits allows you to round the integer 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 that allow you to work with decimals. One of them - ROUNDUP, gives the closest number, more modulo. For example, the expression =ROUNDUP(-10,2,0) will give -11. The number of digits here is 0, which means we get an integer value. nearest integer, greater in modulus, - just -11. Usage example: 
ROUNDDOWN similar to the previous function, but returns the closest value that is smaller in absolute value. The difference in the work of the above means 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 |
We often use rounding in everyday life. If the distance from home to school is 503 meters. We can say, by rounding up the value, that the distance from home to school is 500 meters. That is, we have brought the number 503 closer to the more easily perceived number 500. For example, a loaf of bread weighs 498 grams, then by rounding the result we can say that a loaf of bread weighs 500 grams.
rounding- this is the approximation of a number to a “lighter” number for human perception.
The result of rounding is approximate number. Rounding is indicated by the symbol ≈, such a symbol reads “approximately equal”.
You can write 503≈500 or 498≈500.
Such an entry is read as “five hundred three is approximately equal to five hundred” or “four hundred ninety-eight is approximately equal to five hundred”.
Let's take another example:
44 71≈4000 45 71≈5000
43 71≈4000 46 71≈5000
42 71≈4000 47 71≈5000
41 71≈4000 48 71≈5000
40 71≈4000 49 71≈5000
In this example, numbers have been rounded to the thousands place. If we look at the rounding pattern, we will see that in one case the numbers are rounded down, and in the other - up. After rounding, all other numbers after the thousands place were replaced by zeros.
Number rounding rules:
1) If the figure to be rounded is equal to 0, 1, 2, 3, 4, then the digit of the digit to which the rounding is going does not change, and the rest of the numbers are replaced by zeros.
2) If the figure to be rounded is equal to 5, 6, 7, 8, 9, then the digit of the digit up to which the rounding is going on becomes 1 more, and the remaining numbers are replaced by zeros.
For example:
1) Round to the tens place of 364.
The digit of tens in this example is the number 6. After the six there is the number 4. According to the rounding rule, the number 4 does not change the digit of the tens. We write zero instead of 4. We get:
36 4 ≈360
2) Round to the hundreds place of 4781.
The hundreds digit in this example is the number 7. After the seven is the number 8, which affects whether the hundreds digit changes or not. According to the rounding rule, the number 8 increases the hundreds place by 1, and the rest of the numbers are replaced by zeros. We get:
47 8 1≈48 00
3) Round to the thousands place of 215936.
The thousands place in this example is the number 5. After the five is the number 9, which affects whether the thousands place changes or not. According to the rounding rule, the number 9 increases the thousands place by 1, and the remaining numbers are replaced by zeros. We get:
215 9 36≈216 000
4) Round to the tens of thousands of 1,302,894.
The thousand digit in this example is the number 0. After zero, there is the number 2, which affects whether the tens of thousands digit changes or not. According to the rounding rule, the number 2 does not change the digit of tens of thousands, we replace this digit and all digits of the lower digits with zero. We get:
130 2 894≈130 0000
If a exact value number is unimportant, then the value of the number is rounded off and you can perform computational operations with approximate values. The result of the calculation is called estimation of the result of actions.
For example: 598⋅23≈600⋅20≈12000 is comparable to 598⋅23=13754
An estimate of the result of actions is used in order to quickly calculate the answer.
Examples for assignments on the topic rounding:
Example #1:
Determine to what digit rounding is done:
a) 3457987≈3500000 b) 4573426≈4573000 c) 16784≈17000
Let's remember what are the digits on the number 3457987.
7 - unit digit,
8 - tens place,
9 - hundreds place,
7 - thousands place,
5 - digit of tens of thousands,
4 - hundreds of thousands digit,
3 is the digit of millions.
Answer: a) 3 4 57 987≈3 5 00 000 digit of hundreds of thousands b) 4 573 426 ≈ 4 573 000 digit of thousands c) 16 7 841 ≈17 0 000 digit of tens of thousands.
Example #2:
Round the number to 5,999,994 places: a) tens b) hundreds c) millions.
Answer: a) 5,999,994 ≈5,999,990 b) 5,999,99 4≈6,000,000 6,000,000.
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