When working with tables, there is often a need to round a number in Excel; for this purpose, there are a number of available mathematical functions. But you need to understand the difference between rounding and formatting a cell value. Let's consider all the nuances in more detail...

Any numeric value entered into a cell is displayed in the General format (Main Menu or Cell Format). When a number is formatted, it displays a certain number of decimal places that can be customized (cell format). Those. you can specify any number of decimal places using formatting (the number itself in the cell will not change - the display will change).

Rounding functions ROUND(), ROUNDUP(), ROUNDDOWN()

When data in cells is used by formulas, the program works with its actual value, which may differ from what we see on the monitor (for example, as in cell B1 in the first picture). Numbers are rounded using the functions (formulas) ROUND(), ROUNDUP(), ROUNDDOWN().

An interesting function =ROUND (128;6), to round the number “127” to a multiple of “6” in the formula bar you need to write: =ROUND (128;6), in the final cell we get the number “126”.

Rounding monetary values

Very often, when calculating monetary values in Excel, which uses additional calculations, we get numbers with a large number of decimal places. Currency formats provide only two decimal places, so the value must be brought into proper form by rounding the number in Excel.

To do this, if cell B1 contains numerical indicator RUR 10,561 (this format can be set by clicking the money icon in the second picture), to bring the value to the desired value (2 decimal places), just write in the formula bar: =ROUND (B1;2), we get the result 10.56 rubles.

There are cases when a value needs to be rounded up or down; for this, the following formulas are used:

1. Rounding up, i.e. up: = OVERUP(B1;0.01), cell B1 will receive the value 10.57 rubles, rounded up to the next penny (0.01)
2. Rounding down, down: =OKRVNIZ(B1;0.01), the cell will receive the value of 10.56 rubles, rounded down to the next penny
3. And if, for example, you round the indicator to 10 kopecks, use the formula: =ROADUP(B2,0.10)

Convert to integer

In order to get an integer in Excel, use the formulas =INTEGER() and =RESTRICTION(). At first glance they may seem similar, but this is not the case, this is especially clearly visible in negative numbers. When using a formula with the REMOVE function, only the fractional part of the number is removed.

For example, we have the number - 16.3543, the formula: = SELECT (-16.3543) converts the value to the number -16, and the formula: = INTEGER (-16.3543) gives the indicator -17, because the next integer number is for “-16.3543” is exactly “-17”.

Sometimes the TRUN function is used; to truncate decimal places, the formula: = TRIN (16.3555555;2) gives the indicator “16.35”.

How to round a number up or down in Excel

It happens that large digital values need to be rounded up or down to a certain number of some significant digits. To do this, we use formulas with the functions OKRUP and OKRVBOTT. For example, we have the number 164,358 located in cell B1, the formula: =ROUNDUP (B2;3-LENGTH (B1)), converts it to the indicator “165000”. Three in this formula is exactly the value that is responsible for the number of characters in the transformation. If we replace it with “2” for example and write the formula =ROUNDBOTTOM (B2;2-LENGTH(A1)), we get the value “160000”.

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

Bank rounding

Very often in accounting programs such as 1C, bank rounding is used, as Wikipedia says: Bank rounding(eng. banker’s rounding) or accounting rounding - rounding here occurs to the nearest even number (if the number ends in 5), that is, 2.5 → 2, 3.5 → 4. To do this, you can use the following functions:

Round to even/odd

The =EVEN() function rounds to the nearest even integer. In this case, positive numbers are rounded up, and negative numbers are rounded down.

The =ODD() function rounds a number to the nearest odd integer. Positive numbers are rounded up, negative numbers are rounded down

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Today we will look at a rather boring topic, without understanding which it is not possible to move on. This topic is called “rounding numbers” or in other words “approximate values of numbers.”

Lesson content

Approximate values

Approximate (or approximate) values are used when the exact value of something cannot be found, or the value is not important to the item being examined.

For example, in words one can say that half a million people live in a city, but this statement will not be true, since the number of people in the city changes - people come and leave, are born and die. Therefore, it would be more correct to say that the city lives approximately half a million people.

Another example. Classes start at nine in the morning. We left the house at 8:30. After some time on the road, we met a friend who asked us what time it was. When we left the house it was 8:30, we spent some unknown time on the road. We don’t know what time it is, so we answer our friend: “now approximately about nine o'clock."

In mathematics, approximate values are indicated using a special sign. It looks like this:

Read as "approximately equal."

To indicate the approximate value of something, they resort to such an operation as rounding numbers.

Rounding numbers

To find an approximate value, an operation such as rounding numbers.

The word "rounding" speaks for itself. To round a number means to make it round. A number that ends in zero is called round. For example, the following numbers are round,

10, 20, 30, 100, 300, 700, 1000

Any number can be made round. The procedure by which a number is made round is called rounding the number.

We have already been involved in “rounding” numbers when we divided big numbers. Let us recall that for this we left the digit forming the most significant digit unchanged, and replaced the remaining digits with zeros. But these were just sketches that we made to make division easier. A kind of life hack. In fact, this was not even a rounding of numbers. That is why at the beginning of this paragraph we put the word rounding in quotation marks.

In fact, the essence of rounding is to find the closest value from the original. At the same time, the number can be rounded to a certain digit - to the tens digit, the hundreds digit, the thousand digit.

Let's look at a simple example of rounding. Given the number 17. You need to round it to the tens place.

Without getting ahead of ourselves, let’s try to understand what “round to the tens place” means. When they say to round the number 17, we are required to find the nearest round number for the number 17. Moreover, during this search, changes may also affect the number that is in the tens place in the number 17 (i.e., ones).

Let's imagine that all numbers from 10 to 20 lie on a straight line:

The figure shows that for the number 17 the nearest round number is 20. So the answer to the problem will be like this: 17 is approximately equal to 20

17 ≈ 20

We found an approximate value for 17, that is, we rounded it to the tens place. It can be seen that after rounding, a new digit 2 appeared in the tens place.

Let's try to find an approximate number for the number 12. To do this, imagine again that all numbers from 10 to 20 lie on a straight line:

The figure shows that the nearest round number for 12 is the number 10. So the answer to the problem will be like this: 12 is approximately equal to 10

12 ≈ 10

We found an approximate value for 12, that is, we rounded it to the tens place. This time the number 1, which was in the tens place in the number 12, did not suffer from rounding. We will look at why this happened later.

Let's try to find the closest number for the number 15. Let's imagine again that all numbers from 10 to 20 lie on a straight line:

The figure shows that the number 15 is equally distant from the round numbers 10 and 20. The question arises: which of these round numbers will be the approximate value for the number 15? For such cases, we agreed to take the larger number as an approximate one. 20 is greater than 10, so the approximation for 15 is 20

15 ≈ 20

Large numbers can also be rounded. Naturally, it is not possible for them to draw a straight line and depict numbers. There is a way for them. For example, let's round the number 1456 to the tens place.

We must round 1456 to the tens place. The tens place starts at five:

Now we temporarily forget about the existence of the first numbers 1 and 4. The number remaining is 56

Now we look at which round number is closer to the number 56. Obviously, the closest round number for 56 is the number 60. So we replace the number 56 with the number 60

So, when rounding the number 1456 to the tens place, we get 1460

1456 ≈ 1460

It can be seen that after rounding the number 1456 to the tens place, the changes affected the tens place itself. The new number obtained now has a 6 in the tens place, not a 5.

You can round numbers not only to the tens place. You can also round to the hundreds, thousands, or tens of thousands place.

Once it becomes clear that rounding is nothing more than searching for the nearest number, you can apply ready-made rules that make rounding numbers much easier.

First rounding rule

From the previous examples it became clear that when rounding a number to a certain digit, the low-order digits are replaced by zeros. Numbers that are replaced by zeros are called discarded digits.

The first rounding rule is as follows:

If, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

For example, let's round the number 123 to the tens place.

First of all, we find the digit to be stored. To do this, you need to read the task itself. The digit being stored is located in the digit referred to in the task. The assignment says: round the number 123 to tens place.

We see that there is a two in the tens place. So the stored digit is 2

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after the two is the number 3. This means the number 3 is first digit to be discarded.

Now we apply the rounding rule. It says that if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

That's what we do. We leave the saved digit unchanged, and replace all low-order digits with zeros. In other words, we replace everything that follows the number 2 with zeros (more precisely, zero):

123 ≈ 120

This means that when rounding the number 123 to the tens place, we get the number 120 approximating it.

Now let's try to round the same number 123, but to hundreds place.

We need to round the number 123 to the hundreds place. Again we are looking for the number to be saved. This time the digit being stored is 1 because we are rounding the number to the hundreds place.

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after one is the number 2. This means that the number 2 is first digit to be discarded:

Now let's apply the rule. It says that if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

That's what we do. We leave the saved digit unchanged, and replace all low-order digits with zeros. In other words, we replace everything that follows the number 1 with zeros:

123 ≈ 100

This means that when rounding the number 123 to the hundreds place, we get the approximate number 100.

Example 3. Round 1234 to the tens place.

Here the retained digit is 3. And the first discarded digit is 4.

This means we leave the saved number 3 unchanged, and replace everything that is located after it with zero:

1234 ≈ 1230

Example 4. Round 1234 to the hundreds place.

Here, the retained digit is 2. And the first discarded digit is 3. According to the rule, if, when rounding numbers, the first of the discarded digits is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means we leave the saved number 2 unchanged, and replace everything that is located after it with zeros:

1234 ≈ 1200

Example 3. Round 1234 to the thousands place.

Here, the retained digit is 1. And the first discarded digit is 2. According to the rule, if, when rounding numbers, the first of the discarded digits is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means we leave the stored digit 1 unchanged, and replace everything that is located after it with zeros:

1234 ≈ 1000

Second rounding rule

The second rounding rule is as follows:

When rounding numbers, if the first digit to be discarded is 5, 6, 7, 8, or 9, then the retained digit is increased by one.

For example, let's round the number 675 to the tens place.

We see that there is a seven in the tens place. So the digit being stored is 7

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after seven is the number 5. This means that the number 5 is first digit to be discarded.

Our first discarded digit is 5. This means we must increase the retained digit 7 by one, and replace everything after it with zero:

675 ≈ 680

This means that when rounding the number 675 to the tens place, we obtain the approximate number 680.

Now let's try to round the same number 675, but to hundreds place.

We need to round the number 675 to the hundreds place. Again we are looking for the number to be saved. This time the digit being stored is 6, since we are rounding the number to the hundreds place:

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after six is the number 7. This means that the number 7 is first digit to be discarded:

Now we apply the second rounding rule. It says that when rounding numbers, if the first digit to be discarded is 5, 6, 7, 8, or 9, then the digit retained is increased by one.

Our first discarded digit is 7. This means we must increase the retained digit 6 by one, and replace everything after it with zeros:

675 ≈ 700

This means that when rounding the number 675 to the hundreds place, we get the approximate number 700.

Example 3. Round the number 9876 to the tens place.

Here the retained digit is 7. And the first discarded digit is 6.

This means we increase the stored number 7 by one, and replace everything that is located after it with zero:

9876 ≈ 9880

Example 4. Round 9876 to the hundreds place.

Here the retained digit is 8. And the first discarded digit is 7. According to the rule, if, when rounding numbers, the first of the discarded digits is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means we increase the stored number 8 by one, and replace everything that is located after it with zeros:

9876 ≈ 9900

Example 5. Round 9876 to the thousands place.

Here, the retained digit is 9. And the first discarded digit is 8. According to the rule, if, when rounding numbers, the first of the discarded digits is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means we increase the stored number 9 by one, and replace everything that is located after it with zeros:

9876 ≈ 10000

Example 6. Round 2971 to the nearest hundred.

When rounding this number to the nearest hundred, you should be careful because the digit being retained here is 9, and the first digit to be discarded is 7. This means that the digit 9 must be increased by one. But the fact is that after increasing nine by one, the result is 10, and this figure will not fit into the hundreds digit of the new number.

In this case, in the hundreds place of the new number you need to write 0, and move the unit to the next place and add it with the number that is there. Next, replace all digits after the saved one with zeros:

2971 ≈ 3000

Rounding decimals

When rounding decimal fractions, you should be especially careful because a decimal fraction consists of an integer part and a fractional part. And each of these two parts has its own categories:

Integer digits:

units digit
tens place
hundreds place
thousand digit

Fractional digits:

tenth place
hundredths place
thousandth place

Let's consider decimal 123.456 - one hundred twenty-three point four hundred fifty-six thousandths. Here the integer part is 123, and the fractional part is 456. Moreover, each of these parts has its own digits. It is very important not to confuse them:

The same rounding rules apply for the whole part as for ordinary numbers. The difference is that after rounding the integer part and replacing all digits after the stored digit with zeros, the fractional part is completely discarded.

For example, round the fraction 123.456 to tens place. Exactly until tens place, not tenth place. It is very important not to confuse these categories. Discharge dozens is located in the whole part, and the digit tenths in fractional

We must round 123.456 to the tens place. The digit retained here is 2, and the first digit discarded is 3

According to the rule, if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means that the saved digit will remain unchanged, and everything else will be replaced by zero. What to do with the fractional part? It is simply discarded (removed):

123,456 ≈ 120

Now let's try to round the same fraction 123.456 to units digit. The digit to be retained here will be 3, and the first digit to be discarded is 4, which is in the fractional part:

According to the rule, if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means that the saved digit will remain unchanged, and everything else will be replaced by zero. The remaining fractional part will be discarded:

123,456 ≈ 123,0

The zero that remains after the decimal point can also be discarded. So the final answer will look like this:

123,456 ≈ 123,0 ≈ 123

Now let's start rounding fractional parts. The same rules apply for rounding fractional parts as for rounding whole parts. Let's try to round the fraction 123.456 to tenth place. The number 4 is in the tenths place, which means it is the retained digit, and the first digit to be discarded is 5, which is in the hundredths place:

According to the rule, when rounding numbers, if the first digit to be discarded is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means that the stored digit 4 will increase by one, and the rest will be replaced by zeros

123,456 ≈ 123,500

Let's try to round the same fraction 123.456 to the hundredth place. The digit retained here is 5, and the first digit discarded is 6, which is in the thousandths place:

According to the rule, when rounding numbers, if the first digit to be discarded is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means that the stored digit 5 will increase by one, and the rest will be replaced by zeros

123,456 ≈ 123,460

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This CMEA standard establishes the rules for recording and rounding numbers expressed in the decimal number system.

The rules for recording and rounding numbers established in this CMEA standard are intended for use in regulatory, technical, design and technological documentation.

This CMEA standard does not apply to special rounding rules established in other CMEA standards.

1. RULES FOR RECORDING NUMBERS

1.1. The significant digits of a given number are all the digits from the first non-zero digit on the left to the last recorded digit on the right. In this case, the zeros resulting from the factor 10 n are not taken into account.

	1. Number 12.0	has three significant figures;
	2. Number 30	has two significant figures;
	3. Number 120 10 3	has three significant figures;
	4. Number 0.514 10	has three significant figures;
	5. Number 0.0056	has two significant figures.

1.2. When it is necessary to indicate that a number is exact, the word "exact" must be written after the number or the last significant digit must be printed in bold.

Example. In printed text:

1 kWh = 3,600,000 J (exact), or = 3,600,000 J

1.3. Records of approximate numbers should be distinguished by the number of significant digits.

Examples:

1. It is necessary to distinguish between the numbers 2.4 and 2.40. The entry 2,4 means that only the whole and tenth digits are correct; the true value of the number can be for example 2.43 and 2.38. Writing 2.40 means that hundredths of the number are also correct; the true number may be 2.403 and 2.398, but not 2.421 or 2.382.

2. The entry 382 means that all numbers are correct; if you cannot vouch for the last digit, then the number should be written 3.8·10 2.

3. If in the number 4720 only the first two digits are correct, it should be written 47·10 2 or 4.7·10 3.

1.4. The number for which the permissible deviation is indicated must have the last significant digit of the same digit as the last significant digit of the deviation.

Examples:

1.5. It is advisable to write down the numerical values of a quantity and its error (deviation) indicating the same unit of physical quantities.

Example. 80.555±0.002 kg

1.6. The intervals between numerical values of quantities should be written down:

From 60 to 100 or from 60 to 100

Over 100 to 120 or over 100 to 120

Over 120 to 150 or over 120 to 150.

1.7. Numerical values of quantities must be indicated in standards with the same number of digits, which is necessary to ensure the required performance properties and product quality. The recording of numerical values of quantities up to the first, second, third, etc. decimal place for different standard sizes, types of brands of products of the same name, as a rule, should be the same. For example, if the thickness gradation of a hot-rolled steel strip is 0.25 mm, then the entire range of strip thicknesses must be indicated accurate to the second decimal place.

Depending on the technical characteristics and purpose of the product, the number of decimal places of numerical values of the same parameter, size, indicator or norm may have several stages (groups) and should be the same only within this stage (group).

2. ROUNDING RULES

2.1. Rounding a number is the removal of significant digits on the right to a certain digit with a possible change in the digit of this digit.

Example. Rounding 132.48 to four significant figures becomes 132.5.

2.2. If the first of the discarded digits (counting from left to right) is less than 5, then the last saved digit does not change.

Example. Rounding 12.23 to three significant figures gives 12.2.

2.3. If the first of the discarded digits (counting from left to right) is 5, then the last retained digit is increased by one.

Example. Rounding the number 0.145 to two significant figures gives 0.15.

Note. In cases where the results of previous rounding must be taken into account, proceed as follows:

1) if the discarded digit was obtained as a result of the previous rounding up, then the last saved digit is retained;

Example. Rounding to one significant digit the number 0.15 (resulting from rounding the number 0.149) gives 0.1.

2) if the discarded digit was obtained as a result of the previous rounding down, then the last remaining digit is increased by one (with a transition to the next digits, if necessary).

Example. Rounding the number 0.25 (resulting from the previous rounding of the number 0.252) gives 0.3.

2.4. If the first of the discarded digits (counting from left to right) is greater than 5, then the last retained digit is increased by one.

Example. Rounding the number 0.156 to two significant figures gives 0.16.

2.5. Rounding should be done immediately to the desired number of significant figures, rather than in stages.

Example. Rounding the number 565.46 to three significant figures is done directly by 565. Rounding by stages would result in:

565.46 in stage I - to 565.5,

and in stage II - 566 (wrong).

2.6. Whole numbers are rounded according to the same rules as fractions.

Example. Rounding 12,456 to two significant figures gives 12·10 3 .

Topic 01.693.04-75.

3. The CMEA standard was approved at the 41st meeting of the PCC.

4. Dates for the start of application of the CMEA standard:

CMEA member countries	Deadline for the start of application of the CMEA standard in contractual legal relations on economic, scientific and technical cooperation	Date for the start of application of the CMEA standard in the national economy
NRB	December 1979	December 1979
VNR	December 1978	December 1978
GDR	December 1978	December 1978
Republic of Cuba
MPR
Poland
SRR
USSR	December 1979	December 1979
Czechoslovakia	December 1978	December 1978

5. The date of the first inspection is 1981, the frequency of inspection is 5 years.

When rounding, only sure signs, the rest are discarded.

Rule 1: Rounding is achieved by simply discarding digits if the first digit to be discarded is less than 5.

Rule 2. If the first of the discarded digits is greater than 5, then the last digit is increased by one. The last digit is also incremented when the first digit to be discarded is 5, followed by one or more non-zero digits. For example, various roundings of 35.856 would be 35.86; 35.9; 36.

Rule 3. If the discarded digit is 5, and there are no significant digits behind it, then rounding is done to the nearest even number, i.e. the last digit stored remains unchanged if it is even and increases by one if it is odd. For example, 0.435 is rounded to 0.44; We round 0.465 to 0.46.

8. EXAMPLE OF PROCESSING MEASUREMENT RESULTS

Determination of density of solids. Suppose solid has the shape of a cylinder. Then the density ρ can be determined by the formula:

where D is the diameter of the cylinder, h is its height, m is mass.

Let the following data be obtained as a result of measurements of m, D, and h:

No.	m, g	Δm, g	D, mm	ΔD, mm	h, mm	Δh, mm	, g/cm 3	Δ, g/cm 3
	51,2	0,1	12,68	0,07	80,3	0,15	5,11	0,07	0,013
	12,63	80,2
	12,52	80,3
	12,59	80,2
	12,61	80,1
average			12,61		80,2		5,11

Let's determine the average value of D̃:

Let's find the errors of individual measurements and their squares

Let us determine the root mean square error of a series of measurements:

We set the reliability value α = 0.95 and use the table to find the Student coefficient t α. n =2.8 (for n = 5). We determine the boundaries of the confidence interval:

Since the calculated value ΔD = 0.07 mm significantly exceeds the absolute micrometer error of 0.01 mm (measurement is made with a micrometer), the resulting value can serve as an estimate of the confidence interval limit:

D = D̃ ± Δ D; D= (12.61 ±0.07) mm.

Let's determine the value of h̃:

Hence:

For α = 0.95 and n = 5 Student's coefficient t α, n = 2.8.

Determining the boundaries of the confidence interval

Since the obtained value Δh = 0.11 mm is of the same order as the caliper error, equal to 0.1 mm (h is measured with a caliper), the boundaries of the confidence interval should be determined by the formula:

Hence:

Let's calculate the average density ρ:

Let's find an expression for the relative error:

Where

7. GOST 16263-70 Metrology. Terms and definitions.

8. GOST 8.207-76 Direct measurements with multiple observations. Methods for processing observation results.

9. GOST 11.002-73 (Article CMEA 545-77) Rules for assessing the anomaly of observation results.

Tsarkovskaya Nadezhda Ivanovna

Sakharov Yuri Georgievich

General physics

Guidelines to implementation laboratory work“Introduction to the theory of measurement errors” for students of all specialties

Format 60*84 1/16 Volume 1 academic publication. l. Circulation 50 copies.

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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 are talking about the number 18.4893, then rounding to hundredths occurs as follows: the first digit to be discarded is 3, so no changes occur. 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.