Rounding a number to the required decimal place. How to round numbers up and down with Excel functions

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 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) 4 573 426 ≈ 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.

Many people wonder how to round numbers. This need often arises for people who connect their lives with accounting or other activities that require calculations. Rounding can be done to integers, tenths, and so on. And you need to know how to do it correctly so that the calculations are more or less accurate.

What is a round number anyway? It's the one that ends in 0 (for the most part). In everyday life, the ability to round numbers greatly facilitates shopping trips. Standing at the checkout, you can roughly estimate the total cost of purchases, compare how much a kilogram of the same product costs in packages of different weights. With numbers reduced to a convenient form, it is easier to make mental calculations without resorting to the help of a calculator.

Why are numbers rounded up?

A person tends to round any numbers in cases where more simplified operations need to be performed. For example, a melon weighs 3,150 kilograms. When a person tells his friends about how many grams a southern fruit has, he may be considered not a very interesting interlocutor. Phrases like "So I bought a three-kilogram melon" sound much more concise without delving into all sorts of unnecessary details.

Interestingly, even in science there is no need to always deal with the most accurate numbers. And if we are talking about periodic infinite fractions, which have the form 3.33333333 ... 3, then this becomes impossible. Therefore, the most logical option would be to simply round them. As a rule, the result after that is distorted slightly. So how do you round numbers?

Some important rules for rounding numbers

So, if you want to round a number, is it important to understand the basic principles of rounding? This is a change operation aimed at reducing the number of decimal places. To carry out this action, you need to know a few important rules:

If the number of the required digit is in the range of 5-9, rounding up is carried out.
If the number of the desired digit is between 1-4, rounding down is performed.

For example, we have the number 59. We need to round it up. To do this, you need to take the number 9 and add one to it to get 60. That's the answer to the question of how to round numbers. Now let's consider special cases. Actually, we figured out how to round a number to tens using this example. Now it remains only to put this knowledge into practice.

How to round a number to integers

It often happens that there is a need to round, for example, the number 5.9. This procedure is not difficult. First we need to omit the comma, and when rounding, the already familiar number 60 appears before our eyes. And now we put the comma in place, and we get 6.0. And since zeros in decimals are usually omitted, we end up with the number 6.

A similar operation can be performed with more complex numbers. For example, how do you round numbers like 5.49 to integers? It all depends on what goals you set for yourself. In general, according to the rules of mathematics, 5.49 is still not 5.5. Therefore, it cannot be rounded up. But you can round it up to 5.5, after which rounding up to 6 becomes legal. But this trick does not always work, so you need to be extremely careful.

In principle, an example of the correct rounding of a number to tenths has already been considered above, so now it is important to display only the main principle. In fact, everything happens in approximately the same way. If the digit that is in the second position after the decimal point is within 5-9, then it is generally removed, and the digit in front of it is increased by one. If less than 5, then this figure is removed, and the previous one remains in its place.

For example, at 4.59 to 4.6, the number "9" goes away, and one is added to the five. But when rounding 4.41, the unit is omitted, and the four remains unchanged.

How do marketers use the inability of the mass consumer to round numbers?

It turns out that most people in the world do not have the habit of evaluating the real cost of a product, which is actively exploited by marketers. Everyone knows stock slogans like "Buy for only 9.99". Yes, we consciously understand that this is already, in fact, ten dollars. Nevertheless, our brain is arranged in such a way that it perceives only the first digit. So the simple operation of bringing the number into a convenient form should become a habit.

Very often, rounding allows a better estimate of intermediate successes, expressed in numerical form. For example, a person began to earn $ 550 a month. An optimist will say that this is almost 600, a pessimist - that it is a little more than 500. It seems that there is a difference, but it is more pleasant for the brain to "see" that the object has achieved something more (or vice versa).

There are countless examples where the ability to round is incredibly useful. It is important to be creative and, if possible, not to be loaded with unnecessary information. Then success will be immediate.

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 must use rounding rules.

Underline the digit to which you want to round the number.
Separate all digits to the right of this digit with a vertical bar.
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.
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 digit is the number 8, so we add 1 to the thousands digit (we have it 7), and replace all the digits 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 needs to 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.

Decision. 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.

Decision. 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.

Decision. We underline the number in the hundredth 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.

www.mathematics-repetition.com

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 it 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 guided not 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.

Let's look at examples of how to round up to tenths of a number using the rounding rules.

Rule for rounding numbers to tenths.

To round a decimal to tenths, you must leave only one digit after the decimal point, and discard all other digits following it.

If the first of the discarded digits is 0, 1, 2, 3 or 4, then the previous digit is not changed.

If the first of the discarded digits is 5, 6, 7, 8 or 9, then the previous digit is increased by one.

Examples.

Round to tenths:

To round a number to tenths, leave the first digit after the decimal point, and discard the rest. Since the first discarded digit is 5, we increase the previous digit by one. They read: "Twenty-three point seventy-five hundredths is approximately equal to twenty-three point eight."

To round this number to tenths, leave only the first digit after the decimal point, discard the rest. The first discarded digit is 1, so the previous digit is not changed. They read: "Three hundred and forty-eight point thirty-one hundredth is approximately equal to three hundred and forty-one point three."

Rounding to tenths, we leave one digit after the decimal point, and discard the rest. The first of the discarded digits is 6, which means that we increase the previous one by one. They read: "Forty-nine point, nine hundred and sixty-two thousandths is approximately equal to fifty point, zero tenths."

We round up to tenths, so after the comma we leave only the first of the digits, the rest are discarded. The first of the discarded digits is 4, which means we leave the previous digit unchanged. They read: "Seven point twenty-eight thousandths is approximately equal to seven point zero tenths."

To round to tenths, this number leaves one digit after the decimal point, and discard all following after it. Since the first discarded digit is 7, therefore, we add one to the previous one. They read: "Fifty-six point eight thousand seven hundred and six ten-thousandths is approximately equal to fifty-six point nine-tenths."

And a couple more examples for rounding to tenths:

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 . In the case of a sufficient number of digits after the decimal point, rounding occurs in this way: 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.