How to round the number 3 quarters to tenths. Rounding numbers in Microsoft Excel

We often use rounding in Everyday life. If the distance from home to school is 503 meters. We can say, by rounding 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 we can say by rounding the result that a loaf of bread weighs 500 grams.

Rounding- this is the approximation of a number to an “easier” number for human perception.

The result of rounding is approximate number. Rounding is indicated by the symbol ≈, this symbol reads “approximately equal.”

You can write 503≈500 or 498≈500.

An entry such as “five hundred and three is approximately equal to five hundred” or “four hundred and ninety-eight is approximately equal to five hundred” is read.

Let's look at 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 in this example Numbers were rounded to the thousandth 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 with zeros.

Rules for rounding numbers:

1) If the digit being rounded is 0, 1, 2, 3, 4, then the digit of the place to which the rounding occurs does not change, and the remaining numbers are replaced by zeros.

2) If the digit being rounded is 5, 6, 7, 8, 9, then the digit of the place to which the rounding occurs becomes 1 more, and the remaining numbers are replaced by zeros.

For example:

1) Round 364 to the tens place.

The tens place 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 tens place. We write zero instead of 4. We get:

36 4 ≈360

2) Round 4,781 to the hundreds place.

The hundreds place in this example is the number 7. After the seven there is the number 8, which affects whether the hundreds place changes or not. According to the rounding rule, the number 8 increases the hundreds place by 1, and the remaining numbers are replaced with zeros. We get:

47 8 1≈48 00

3) Round to the thousandth place the number 215,936.

The thousands place in this example is the number 5. After the five there is the number 9, which affects whether the thousand 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 place the number 1,302,894.

The thousands place in this example is the number 0. After the zero there is a 2, which affects whether the tens of thousands place changes or not. According to the rounding rule, the number 2 does not change the tens of thousands digit; we replace this digit and all lower digits with zero. We get:

130 2 894≈130 0000

If exact value numbers are unimportant, then the value of the number is rounded and you can perform computational operations with approximate values. The result of the calculation is called an estimate 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 to quickly calculate the answer.

Examples for assignments on rounding:

Example #1:
Determine to what digit the rounding is done:
a) 3457987≈3500000 b)4573426≈4573000 c)16784≈17000
Let's remember what digits there are in the number 3457987.

7 – units digit,

8 – tens place,

9 – hundreds place,

7 – thousand place,

5 – tens of thousands place,

4 – hundreds of thousands place,
3 – million digit.
Answer: a) 3 4 57 987≈3 5 00 000 hundred thousand place b) 4 573 426≈4 573 000 thousand place c)16 7 841≈17 0 000 ten thousand place.

Example #2:
Round the number to the digits 5,999,994: a) tens b) hundreds c) millions.
Answer: a) 5 999 994 ≈5 999 990 b) 5 999 99 4≈6 000 000 (since the digits of hundreds, thousands, tens of thousands, hundreds of thousands are number 9, each digit has increased by 1) 5 9 99 994≈ 6,000,000.

Fractional numbers in Excel spreadsheets can be displayed with 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 menu that opens, select “ Cell format...", then the tab " Number", select the format " Numerical", we determine how many decimal places there will be after the decimal point (2 places are suggested by default);
Click the cell on the “ tab home» select « Numerical", or go to " Other number formats..." and set it up there.

This is what the fraction 0.129 looks like if you change the number of decimal places after the decimal point in the cell format:

Please note that A1,A2,A3 contain the same thing meaning, only the presentation form changes. In further calculations, not the value visible on the screen will be used, but original. This can be a little confusing for a novice spreadsheet user. To actually change the value, you need to use special functions; there are several of them in Excel.

Formula rounding

One of the commonly used rounding functions is ROUND. It works according to standard mathematical rules. Select a cell and click the “ Insert function", category " Mathematical", we find ROUND

We define the arguments, there are two of them - itself fraction And quantity discharges. Click " OK» and see what happened.

For example, the expression =ROUND(0.129,1) will give the result 0.1. A zero number of digits allows you to get rid of the fractional part. Selecting 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, is just -11. Usage example:

ROUND BOTTOM similar to the previous function, but produces the closest value, smaller in absolute value. The difference in the operation of the above-described means can be seen from examples:

=ROUND(7.384,0)	7
=ROUNDUP(7.384,0)	8
=ROUNDBOTTOM(7.384,0)	7
=ROUND(7.384,1)	7,4
=ROUNDUP(7.384,1)	7,4
=ROUNDBOTTOM(7.384,1)	7,3

In approximate calculations, it is often necessary to round some numbers, both approximate and exact, that is, remove one or more ending digits. To ensure that an individual rounded number is as close as possible to the number being rounded, certain rules must be followed.

If the first of the separated digits is greater than the number 5, then the last of the remaining digits is amplified, in other words, increased by one. Strengthening is also assumed when the first of the removed digits is equal to 5, and after it there is one or a certain number significant figures.

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

The number 45.254 is rounded down as – 45.3. Here the digit 2 will be boosted to 3 because the first digit cut off is 5 and 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 down as – 46. The number 46 is closest to the number being rounded 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 digit retained remains unchanged if it is even, and is strengthened if it is odd.

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

The number 0.935 is rounded down as – 0.94. The last digit left, 3, is strengthened since it is odd.

Rounding numbers

Numbers are rounded when complete accuracy is not needed or possible.

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

Natural numbers are rounded to tens, hundreds, thousands, etc. Names of numbers in ranks natural number You can remember the topic of natural numbers.

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

If a number is rounded to tens, then we replace the digit in the ones place with zeros.

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

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

Record the rounding result after special sign"≈". This sign reads “approximately equal.”

When rounding a natural number to any digit, you must use rounding rules.

Underline the digit of the place to which the number should be rounded.
Separate all numbers to the right of this digit with a vertical line.
If there is a 0, 1, 2, 3 or 4 to the right of the underlined digit, then all digits that are separated to the right are replaced with zeros. We leave the digit to which we rounded unchanged.
If there is a digit 5, 6, 7, 8 or 9 to the right of the underlined digit, then all digits that are separated to the right are replaced with zeros, and 1 is added to the place digit to which they were rounded.

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

After the underlined digit there is the number 8, which means we add 1 to the thousand digit (for us it is 7), and replace all digits separated by a vertical bar with zeros.

Now let's round 756,485 to hundreds.

Let's round 364 to tens.

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

On the number line, the number 364 is enclosed between two "round" numbers 360 and 370. These two numbers are called approximations of the number 364, accurate to tens.

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

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

Rounded results are often written without the zeros, adding the abbreviation "thousands." (thousand), "million" (million) and "billion." (billion).

8,659,000 = 8,659 thousand
3,000,000 = 3 million.

Rounding is also used to estimate the answer in calculations.

Before accurate calculation Let's 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 make estimates by rounding when dividing numbers.

In some cases, exact number when dividing a certain amount by a specific number it is impossible to determine 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 this number should be reduced to a certain digit, for example, to an integer or to a number with a decimal place. If we reduce 3.3333333333…..3 to an integer, we get 3, and if we reduce 3.3333333333…..3 to a number with a decimal place, we get 3.3.

Rounding rules

What is rounding? This is discarding a few digits that are the last in the series of an exact number. So, following our example, we discarded all the last digits to get the integer (3) and discarded the digits, leaving only the tens places (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 medical supplies, the amount of each of the ingredients of the medicine is taken with the greatest precision, since even a thousandth of a gram can be fatal. If it is necessary to calculate the progress of students at school, then most often a number with a decimal or hundredth place is used.

Let's look at another example where rounding rules apply. For example, there is a number 3.583333 that needs to be rounded to thousandths - after rounding, we should be left with three digits after the decimal point, that is, the result will be the number 3.583. If we round this number 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 of 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 digit to be stored remains unchanged. These rules for rounding numbers apply regardless of whether to a whole number or to tens, hundredths, etc. you need to round the number.

In most cases, when you need 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 specifically to such cases. Let's look at an example. It is necessary to round the number 3.25 to the nearest tenth. Applying the rules for rounding numbers, we get the result 3.2. That is, if there is no digit after “five” or there is a zero, then the last digit remains unchanged, but only if it is even - in our case, “2” is an even digit. If we were to round 3.35, the result would be 3.4. Because, in accordance with the rules of rounding, 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 the last stored digit is followed by the values of digits from 0 to 4, the stored digit does not change. If there are other digits, the last digit is increased by 1.

5.5.7. Rounding numbers

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

Examples.

Round to whole numbers:

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

Solution. We underline the number in the units (integer) place and look at the number behind it. If this is the number 0, 1, 2, 3 or 4, then we leave the underlined number unchanged, and discard all the numbers after it. If the underlined number is followed by the number 5 or 6 or 7 or 8 or 9, then we will increase the underlined number 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 the nearest tenth:

6) 0, 246; 7) 41,253; 8) 3,81; 9) 123,4567; 10) 18,962.

Solution. We underline the number in the tenths place, and then proceed according to the rule: we discard everything after the underlined number. If the underlined number was followed by the number 0 or 1 or 2 or 3 or 4, then we do not change the underlined number. 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. Behind nine there is a six, therefore, we increase nine by 1. (9+1=10) we write zero, 1 goes to the next digit and it will be 19. We just can’t write 19 in the answer, since it should be clear that we rounded to tenths - the number must be in the tenths place. Therefore, the answer is: 19.0.

Round to the nearest hundredth:

11) 2, 045; 12) 32,093; 13) 0, 7689; 14) 543, 008; 15) 67, 382.

Solution. We underline the digit in the hundredths place and, depending on which digit comes after the underlined one, leave the underlined digit unchanged (if it is followed by 0, 1, 2, 3 or 4) or increase the underlined digit 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 answer should contain a number in the digit to which you rounded.

www.mathematics-repetition.com

How to round a number to a whole number

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

Rule for rounding a number to a whole number

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

If the first digit discarded is 0, 1, 2, 3 or 4, then the number will not change.

If the first digit dropped is 5, 6, 7, 8, or 9, the previous digit must be increased by one.

Round the number to the nearest integer:

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

When rounding a number to the nearest integer, we discard the comma and all numbers following it. Since the first of the discarded digits is equal to 8, we increase the previous one 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 the nearest integer, we discard the comma and all numbers following 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 point.”

We discard the comma and all numbers after it. The first of the discarded digits is 3, so we do not change the previous digit. They read: “Zero point three ninety-seven thousandths is approximately equal to zero point.”

The first of the discarded digits is 7, which means that the digit in front of it is increased by one. They read: “Thirty-nine point seven hundred and four thousandths is approximately equal to forty whole.” And a couple more examples for rounding numbers to integers:

27 Comments

Wrong theory about if the number 46.5 is not 47 but 46, this is also called bank rounding to the nearest even number; it is rounded if there is 5 after the decimal point and there is no number after it

Dear ShS! Perhaps(?), rounding in banks follows different rules. I don't know, I don't work in a bank. This site talks about the rules that apply in mathematics.

how to round the number 6.9?

To round a number to an integer, you need to discard all the numbers after the decimal point. We discard 9, so the previous number should be increased by one. This means that 6.9 is approximately equal to seven whole numbers.

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

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

Tell me how to round 46.466667. Confused

If you need to round a number to an integer, then you need to 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 very familiar with the rules of mathematics.

Rule. If the digit 5 is discarded and there are no significant digits behind it, then rounding is done to the nearest even number, i.e., the last digit retained is left unchanged if it is even and strengthened if it is odd.

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

Dear guest! Let it be known that in mathematics there are numbers for rounding various ways rounding. At school they study one of them, which consists in discarding the lower digits of a number. I’m glad for you that you know another way, but it would be nice not to forget your school knowledge.

Thank you very much! It was necessary to round 349.92. That turns out to be 350. Thanks for the rule?

how to round 5499.8 correctly?

If we are talking about rounding to a whole number, then discard all numbers after the decimal point. The discarded digit is 8, therefore, we increase the previous one by one. This means that 5499.8 is approximately equal to 5500 integers.

Good day!
Now this question arose:
There are three numbers: 60.56% 11.73% and 27.71% How to round up to whole numbers? So that the total remains 100. If you simply round, then 61+12+28=101 There is a discrepancy. (If, as you wrote, using the “banking” method, in this case it will work, but in the case of, for example, 60.5% and 39.5%, something will fall again - we will lose 1%.) What should I do?

ABOUT! the method from “guest 07/02/2015 12:11″ helped
Thank you"

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

Perhaps you were taught this way.

0.855 to hundredths please help

0.855≈0.86 (5 is discarded, the previous digit is increased by 1).

Round 2.465 to a whole number

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

How to round 2.4456 to a whole number?

2.4456 ≈ 2 (since the first digit discarded 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 this true?

No. If you need to round 1.45 to a whole number, discard the first digit after the decimal point. Since this is 4, we do not change the previous digit. Thus, 1.45≈1.

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

Examples.

Round to whole numbers:

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

1) 12 ,5≈13;

2) 28 ,49≈28;

3) 0 ,672≈1;

4) 547 ,96≈548;

5) 3 ,71≈4.

Round to the nearest tenth:

6) 0, 246; 7) 41,253; 8) 3,81; 9) 123,4567; 10) 18,962.

6) 0, 2 46≈0,2;

7) 41,2 53≈41,3;

8) 3,8 1≈3,8;

9) 123,4 567≈123,5;

Round to the nearest hundredth:

11) 2, 045; 12) 32,093; 13) 0, 7689; 14) 543, 008; 15) 67, 382.

11) 2, 04 5≈2,05;

12) 32,09 3≈32,09;

13) 0, 76 89≈0,77;

14) 543, 00 8≈543,01;

15) 67, 38 2≈67,38.

Important: the last answer should contain a number in the digit to which you rounded.

Mathematics. 6 Class. Test 5 . Option 1 .

1. Infinite decimal non-periodic fractions are called... numbers.

A) positive; IN) irrational; WITH) even; D) odd; E) rational.

2 . When rounding a number to any digit, all digits following this digit are replaced with zeros, and if they are after the decimal point, they are discarded. If the first digit replaced by a zero or discarded is 0, 1, 2, 3 or 4, then the digit preceding it is not changed. If the first digit replaced by a zero or discarded is 5, 6, 7, 8 or 9, then the digit preceding it is increased by one. Round number to tenths 9,974.

A) 10,0;B) 9,9; C) 9,0; D) 10; E) 9,97.

3. Round number to tens 264,85 .

A) 270; B) 260;C) 260,85; D) 300; E) 264,9.

4 . Round to whole number 52,71.

A) 52; B) 52,7; C) 53,7; D) 53; E) 50.

5. Round to the nearest thousand 3, 2573 .

A) 3,257; B) 3,258; C) 3,28; D) 3,3; E) 3.

6. Round number to hundreds 49,583 .

A) 50;B) 0; C) 100; D) 49,58;E) 49.

7. An infinite periodic decimal fraction is equal to an ordinary fraction whose numerator is the difference between the entire number after the decimal point and the number after the decimal point before the period; and the denominator consists of nines and zeros, and there are as many nines as there are digits in the period, and as many zeros as there are digits after the decimal point before the period. 0,58 (3) to ordinary.

8. Convert an infinite periodic decimal fraction 0,3 (12) to ordinary.

9. Convert an infinite periodic decimal fraction 1,5 (3) into a mixed number.

10. Convert an infinite periodic decimal fraction 5,2 (144) into a mixed number.

11. Any rational number can be written down Write down the number 3 as an infinite periodic decimal fraction.

A) 3,0 (0);IN) 3,(0); WITH) 3;D) 2,(9); E) 2,9 (0).

12 . Write down common fraction ½ as an infinite periodic decimal fraction.

A) 0,5; B) 0,4 (9); C) 0,5 (0); D) 0,5 (00); E) 0,(5).

You will find answers to the tests on the “Answers” page.

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To consider the peculiarities 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, you must 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 we 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 digit that comes after the hundredths is not rounded, so it is simply discarded.
If we're talking about 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 the nearest hundredth. 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 the nearest hundredth, we see that the number 7 rounds the previous ones. We get 65.00.

How to round numbers to whole numbers

The situation is the same when rounding numbers to integers. If we have, for example, 25.5, then after rounding we get 26. In the case of a sufficient number of decimal places, rounding occurs as follows: after rounding 4.371251 we get 4.

Rounding to tenths occurs in the same way as with 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 could round 13.6734 to get 13.7.

It is important to pay attention to the number that is located before the one that is cut off. For example, if we have a number of 1.450, then after rounding we get 1.4. However, in the case of 4.851, it is advisable to round to 4.9, since after the five there is still a unit.