In approximate calculations, it is often necessary to round some numbers, both approximate and exact, that is, to remove one or more final digits. In order to ensure that a single rounded number is as close as possible to the number being rounded, certain rules must be observed.

If the first of the separated digits is greater than the number 5, then the last of the remaining digits is strengthened, in other words, it increases by one. Gain is also assumed when the first of the removed digits is 5 , followed by one or more significant digits.

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

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

If the first of the cut off digits is less than 5 , then no amplification is performed.

The number 46.48 is rounded off as - 46. The number 46 is closest to the rounded number 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 remaining digit remains unchanged if it is even, and amplifies if it is odd.

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

The number 0.935 is rounded off as - 0.94. The last digit left, 3, is reinforced because it is odd.

Rounding numbers

Numbers are rounded when full precision is not needed or possible.

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

Natural numbers are rounded up to tens, hundreds, thousands, etc. The names of the digits in the digits of a natural number can be recalled in the topic of natural numbers.

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

If the number is rounded to tens, then zeros replace the digit in the unit digit.

If a number is rounded to the nearest hundred, then zero must be in both the units and tens places.

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

Record the rounding result after the special sign "≈". This sign is read as "approximately equal".

When rounding a natural number to some digit, you need to use rounding rules.

1. Underline the digit to which you want to round the number.
2. Separate all digits to the right of this digit with a vertical bar.
3. If the number 0, 1, 2, 3 or 4 is to the right of the underlined digit, then all digits that are separated to the right are replaced by zeros. The digit of the category to which rounding is left unchanged.
4. If the number 5, 6, 7, 8 or 9 is to the right of the underlined digit, then all the digits that are separated to the right are replaced by zeros, and 1 is added to the digit of the digit to which they were rounded.

Let's explain with an example. Let's round 57,861 to the nearest thousand. Let's follow the first two points from the rounding rules.

After the underlined number, there is the number 8, so we add 1 to the thousands digit (we have it 7), and replace all the numbers separated by a vertical bar with zeros.

Now let's round 756,485 to the nearest hundred.

Let's round 364 to tens.

3 6 |4 ≈ 360 - there is 4 in the units place, so we leave 6 in the tens place unchanged.

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

The number 360 is approximate deficient value, and the number 370 is approximate excess value.

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

Rounded results are often written without zeros, adding the abbreviations "thousands." (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 exact calculation, we will estimate the answer by rounding the factors 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 when dividing numbers.

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 items in other situations. Then the given number should be reduced to a certain digit, for example, to an integer or to a number with a decimal place. If we convert 3.3333333333…..3 to an integer, we get 3, and if we convert 3.3333333333…..3 to a number with a decimal place, we get 3.3.

Rounding rules

What is rounding? This is the discarding of several digits that are the last in a series of exact numbers. So, following our example, we discarded all the last digits to get an integer (3) and discarded the digits, leaving only the tens digits (3,3). The number can be rounded to hundredths and thousandths, ten thousandths and other numbers. It all depends on how accurate the number needs to be. 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 of a gram can be fatal. If it is necessary to calculate the performance of students at school, then most often a number with a decimal or hundredth place is used.

Let's look at another example that uses rounding rules. For example, there is a number 3.583333, which must be rounded to thousandths - after rounding, we should have three digits behind the comma, 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, since after “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 stored digit remains unchanged. Such rules for rounding numbers apply regardless of whether they are up to an integer or up to tens, hundredths, etc. you need to round the number.

In most cases, if it is necessary to round a number in which the last digit is "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. You need to round the number 3.25 to tenths. Applying the rules for rounding numbers, we get the result 3.2. That is, if after “five” there is no digit 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 3.35, the result would be 3.4. Since, in accordance with the rounding rules, if there is an odd digit before the “5” that must be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after the “5”. In many cases, simplified rules can be applied, according to which, if there are digits from 0 to 4 after the last stored digit, the stored digit does not change. If there are other digits, the last digit is incremented by 1.

5.5.7. Rounding numbers

To round a number to a certain digit, we underline the digit of this digit, and then we replace all the digits behind the underlined one with zeros, and if they are after the decimal point, we discard. If the first zero-replaced or discarded digit is 0, 1, 2, 3 or 4, then the underlined number leave unchanged. If the first zero-replaced or discarded digit is 5, 6, 7, 8 or 9, then the underlined number increase by 1.

Examples.

Round to whole:

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

Solution. We underline the number in the units (integer) category and look at the number behind it. If this is the number 0, 1, 2, 3 or 4, then the underlined number is left unchanged, and all the numbers after it are discarded. 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 that is in the category of tenths, and then we act according to the rule: we discard all those after the underlined number. If the underlined digit was followed by the number 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 \u003d 10) we write zero, 1 goes to the next digit and it will be 19. We just cannot write 19 in the answer, since it should be clear that we rounded up to tenths - the figure in the category of tenths 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 number in the hundredths place and, depending on which digit is after the underlined one, leave the underlined number unchanged (if it is followed by 0, 1, 2, 3 or 4) or increase the underlined number 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: the last digit in the answer should be the digit in the digit to which you rounded.

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How to round a number to an integer

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

Rule for rounding a number to an integer

To round a number to an integer (or round a number to units), you must discard the comma and all numbers after the decimal point.

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 a number to an integer:

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

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

When rounding a number to an integer, we discard the comma and 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 point."

The first of the discarded digits is 7, which means that we increase the digit in front of it by one. They read: "Thirty-nine point seven hundred and four thousandths is approximately equal to forty point." 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 banking rounding to the nearest even rounded if after the decimal point 5 and there is no number after it

Dear ShS! Perhaps (?), In banks, rounding occurs according to other rules. I don't know, I don't work in a bank. This site is about the rules that apply in mathematics.

how to round the number 6.9?

To round a number to an integer, you must discard all numbers after the decimal point. We discard 9, so the previous number should be increased by one. So 6.9 is approximately equal to seven integers.

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

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

Please tell me how to round 46.466667. confused

If you want to round a number to an integer, then you must discard all the digits after the decimal point. The first of the discarded digits is 4, so we do not change the previous digit:

Dear Svetlana Ivanovna, You are not familiar with the rules of mathematics.

Rule. If the digit 5 ​​is discarded, and there are no significant figures behind it, then rounding is performed to the nearest even number, i.e. the last digit stored is left unchanged if it is even, and amplifies if it is odd.

And Accordingly: Rounding the number 0.0465 to the third decimal place, we write 0.046. We do not make amplifications, since the last saved digit 6 is even. The number 0.046 is as close to the given value as 0.047.

Dear guest! Let it be known to you, in mathematics there are various rounding methods for rounding a number. At school, they study one of them, which consists in discarding the lower digits of the 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 5499.8 correctly?

If we are talking about rounding to an integer, then discard all the numbers after the decimal point. The discarded figure is 8, therefore, we increase the previous one by one. So 5499.8 is approximately equal to 5500 integers.

Good day!
But this question arose seyas:
There are three numbers: 60.56% 11.73% and 27.71% How to round up to whole numbers? That in the sum that 100 remained. If you just round up, then 61+12+28=101 There is a problem. (If, as you wrote, according to the “banking” method, in this case it will work, but in the case, for example, 60.5% and 39.5%, something will fall again - we will lose 1%). How to be?

O! the method from "guest 02.07.2015 12:11" helped
Thanks to"

I don't know, they taught me this in school:
1.5 => 1
1.6 => 2
1.51 => 2
1.51 => 1.6

Maybe that's how you were taught.

0, 855 to hundredths please help

0, 855≈0.86 (discarded 5, increase the previous figure by 1).

Round 2.465 to whole number

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

How to round 2.4456 to an integer?

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

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

No. If you want to round 1.45 to an integer, discard the first digit after the decimal point. Since it's 4, we don't change the previous digit. Thus, 1.45≈1.

The rounding of a natural number is understood as replacing it with such a number that is closest in value, in which one or several last digits in its record are replaced by zeros.

Rounding rule:

To round a natural number, you need to select the digit in the number entry to which rounding is performed.

The number written in the selected digit:

• does not change if the digit following it on the right is 0, 1, 2, 3 or 4;

All digits to the right of this bit are replaced by zeros.

Example: 14 3 ≈ 140 (rounded to the nearest tens);
56 71 ≈ 5700 (rounded to the nearest hundred).

If the digit to which rounding is performed contains the number 9 and it is necessary to increase it by one, then the digit 0 is written in this digit, and the digit in the adjacent high-order digit (on the left) is increased by 1.

Example: 79 6 ≈ 800 (rounded to tens);
9 70 ≈ 1000 (rounded to the nearest hundred).

Rounding decimals

To round a decimal fraction, you need to select the digit in the number entry to which rounding is performed. The number written in this category:

• increments by one if the next digit to the right is 5,6,7,8, or 9.

All digits to the right of this bit are replaced by zeros. If these zeros are in the fractional part of the number, then they are not written.

Example: 143,6 4 ≈ 143.6 (rounded to tenths);
5,68 7 ≈ 5.69 (rounded to hundredths);
27 .945 ≈ 28 (rounded to the nearest integer).

If the digit 9 is in the digit to which rounding is performed and it is necessary to increase it by one, then the digit 0 is written in this digit, and the digit in the previous digit (on the left) is increased by 1.

Example: 8 9, 6 ≈ 90 (rounded to tens);
0,09 7 ≈ 0.10 (rounded to hundredths).

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Rounding numbers

1) Rules for rounding natural numbers. Natural numbers are rounded to units of a certain digit. To round a natural number to units of a certain digit means to establish how many units of this digit are contained in a given number. For example, we want to round the number 237456 to the nearest thousand. This means to find out how many thousands there are in this number. Obviously, it has 237 thousand. How did we know? To do this, we all the digits of a given number up to the thousands place, i.e. hundreds, tens and ones, replaced with zeros and got the number 237000, which can be written in short like this: 237 thousand. But you can, knowing that 1000=10 3, write this rounded number like this: 237 * 10 3 .

So, 237456? 237 thousand or 237 456? 237*10 3 .

Please note that here we did not put the usual equal sign, but approximate equal sign (?).

Why such a sign? Yes, because the numbers 237,456 and 237 thousand are not equal, the second number is slightly less than the first, namely less than 456, therefore, replacing the number 237,456 with the number 237 thousand, we thereby make an error equal to 456, which means that the numbers 237,456 and 237,000 are only approximately equal. Therefore, the sign of approximate equality is put. Note that the error in rounding the number 237,456 to thousands was 456 units, which is less than half of one thousand. Therefore, if we need to round the number 237 873 to thousands, then it is more reasonable to take 237 thousand as the rounded value of the number 237 873, then we will allow an error equal to 873, which is more than half a thousand, i.e. 500. If the rounded value is 238 thousand, then the error will be only 127, which is much less than half a thousand. From these examples, we can deduce the following the general rule for rounding natural numbers to units of a certain digit: replace all digits to the right of this digit with zeros. If the first digit on the left of those replaced by zeros is less than 5, then the rounding is completed and the resulting rounded number can be written in an abbreviated form. If it is equal to or greater than 5, then the digit of the digit to which rounding was performed is replaced by a larger one.

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Rounding natural numbers.

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:

4 4 71≈4000 4 5 71≈5000

4 3 71≈4000 4 6 71≈5000

4 2 71≈4000 4 7 71≈5000

4 1 71≈4000 4 8 71≈5000

4 0 71≈4000 4 9 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.

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:

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:

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:

21 5 9 36≈21 6 000

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:

13 0 2 894≈13 0 0000

If the exact value of the number is not important, 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 57 3 426 ≈ 4 57 3 000 digit of thousands c) 1 6 7 841 ≈ 1 7 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 99 4 ≈5 999 990 b) 5 999 9 9 4 ≈6 000 000 994≈6,000,000.

Rules for rounding natural numbers

Rules for rounding natural numbers.
Rounding a number up to some digit.

From time to time, the country conducts a census of the population. Every day people are born, die, change their place of residence, so the number of inhabitants is constantly changing. Let's say that there are 34,489 inhabitants in one city. Accordingly, when people move in this number, the numbers of the digits of units, tens and even hundreds will change. Such numbers are replaced with zeros, and we get a simpler number. It can be said that he lives in the city approximately 34,000 inhabitants.

Number 34 489 rounded up to 3 thousand 4 000.
If we want to round some number, then we apply the rule:
45|245 - the line shows to what digit we want to round.

If the first digit following the digit to which the number is rounded (to the right of the bar) is 5, 6, 7, 8, 9, then the last remaining digit is increased by 1, and the rest of the digits after the line are replaced by zeros. In other cases, the last remaining digit is not changed.

The given number and the number obtained by rounding it approximately equal.This is written with the sign » » «.
45|245 » 45,000, since the digit following the thousands place is 2.
124 7 | 89 » 124 800, since the digit following the hundreds place is 8.

Round the numbers 12,344; 12,343; 12,342; 12 340; 12,341 to tens.
.

Rounding of natural numbers is used when calculating the price. Subtractions are made orally, an estimate of the result is made. For example:
358 56 = 20,048

For simplified multiplication, round each number:
358 » 400 and 56 » 60 400 x 60 = 24 000

It can be seen that this answer is approximately equal to the first answer.

1. Give examples where you can use rounding numbers..
.
.

2. Explain to what digit the numbers are rounded. The first column has been rounded to the nearest tens. The second column has been rounded to the nearest thousand.

6789 » 6800 . 12 897 » 10 000 .
12 544 » 12 500 . 2 344 672 » 2 340 000 .
245 673 » 245 700 . 78 358 » 78 360 .
26 577 » 30 000 . 34 057 123 » 34 100 000 .

Rounding numbers

Numbers are rounded when full precision is not needed or possible.

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

Natural numbers are rounded up to tens, hundreds, thousands, etc. The names of the digits in the digits of a natural number can be recalled in the topic of natural numbers.

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

If the number is rounded to tens, then zeros replace the digit in the unit digit.

If a number is rounded to the nearest hundred, then zero must be in both the units and tens places.

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

Record the rounding result after the special sign "≈". This sign is read as "approximately equal".

When rounding a natural number to some digit, you need to use rounding rules.

1. Underline the digit to which you want to round the number.
2. Separate all digits to the right of this digit with a vertical bar.
3. If the number 0, 1, 2, 3 or 4 is to the right of the underlined digit, then all digits that are separated to the right are replaced by zeros. The digit of the category to which rounding is left unchanged.
4. If the number 5, 6, 7, 8 or 9 is to the right of the underlined digit, then all the digits that are separated to the right are replaced by zeros, and 1 is added to the digit of the digit to which they were rounded.

Let's explain with an example. Let's round 57,861 to the nearest thousand. Let's follow the first two points from the rounding rules.

After the underlined number, there is the number 8, so we add 1 to the thousands digit (we have it 7), and replace all the numbers separated by a vertical bar with zeros.

Now let's round 756,485 to the nearest hundred.

Let's round 364 to tens.

3 6 |4 ≈ 360 - there is 4 in the units place, so we leave 6 in the tens place unchanged.

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

The number 360 is approximate deficient value, and the number 370 is approximate excess value.

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

Rounded results are often written without zeros, adding the abbreviations "thousands." (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 exact calculation, we will estimate the answer by rounding the factors 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 when dividing numbers.

Let's say you want to round a number to the nearest whole number because you don't care about decimal values, or you want to express a number as a power of 10 to make it easier to approximate calculations. 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 following list contains general rules to consider 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 a positive number, the function 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 desired number of significant digits. 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 want 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.

Numbers are also rounded to other digits - tenths, hundredths, tens, hundreds, etc.




If the number is rounded to some digit, then all the digits following this digit are replaced with zeros, and if they are after the decimal point, then they are discarded.




Rule number 1. If the first of the discarded digits is greater than or equal to 5, then the last of the retained digits is amplified, that is, increased by one.




Example 1. Given the number 45.769, which must be rounded to tenths. The first discarded digit is 6 ˃ 5. Consequently, the last of the stored digits (7) is amplified, i.e., increased by one. And so the rounded number would be 45.8.




Example 2. Given the number 5.165, which must be rounded to hundredths. The first discarded digit is 5 = 5. Therefore, the last of the stored digits (6) is amplified, that is, it increases by one. And so the rounded number would be 5.17.




Rule number 2. If the first of the discarded digits is less than 5, then no gain is made.




Example: The number 45.749 is given and needs to be rounded to tenths. The first discarded digit is 4


Rule number 3. If the discarded digit is 5, and there are no significant digits after it, then rounding is performed to the nearest even number. That is, the last digit remains unchanged if it is even and increases if it is odd.




Example 1: Rounding the number 0.0465 to the third decimal place, we write - 0.046. We do not make amplifications, because the last saved digit (6) is even.




Example 2. Rounding the number 0.0415 to the third decimal place, we write - 0.042. We make amplifications, because the last saved digit (1) is odd.

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

How to round numbers to hundredths

• To round a number to hundredths, it is necessary to 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 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 number after the hundredths is not rounded, so it is simply discarded.
• If we are talking about the number 18.4893, then rounding to hundredths occurs as follows: the first digit to be discarded is 3, so no change occurs. It turns out 18.48.
• In the case of the number 0.2254, we have the first digit, which is discarded when rounding 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 cases when rounding changes all the digits in a number. For example, to round the number 64.9972 to hundredths, we see that the number 7 rounds the previous ones. We get 65.00.

How to round numbers to integers

When rounding numbers to integers, the situation is the same. If we have, for example, 25.5 , then after rounding we get 26 . If there are enough digits after the decimal point, the rounding goes like this: after rounding 4.371251, we get 4 .

Rounding to tenths occurs in the same way as in the case of hundredths. For example, if we need to round 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, you can round 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 after the five there is still one.