## Introduction

Numbers are really commonly provided in ours day come day life. In general, we need not state the precise number as response to the question which calls for us to tell about how many. In various other words, in bespeak to lull our calculations, we often approximate the numbers to part extent. It help us provide approximate answer where specific values space not required. Because that instance, we may say the there are roughly 600 college student in a school. That does not necessarily average that there are precisely 600 students in a school. The exact variety of students in the school might be somewhere about 600 which, for convenience, we have actually rounded off to 600. Rounding off is likewise termed together a faster way method. Another example deserve to be if girlfriend plan an event at house you deserve to just calculation the variety of guests that are supposed to attend the event. It have the right to be a rough estimate the the number of people speak 200. This walk not average that specifically 200 human being will attend the event. This means we deserve to round off numbers come the nearest ar value, say 10, 100, 1000 etc.

You are watching: Round 22 to the nearest ten

Let us learn what we average by round off off come the nearest 10. Allow us discover out.

## How carry out we round off a number to the nearest 10?

Consider two numbers 22 and 29. If we plot these numbers top top a number line we uncover that both 22 and also 29 lies in between 20 and also 30. Also, 22 is nearer to 20 while 29 is nearer to 30. So, we round turn off 22 come 20. Correct to the nearest tens. If we think about 29, us round turn off it come the nearest 10 i beg your pardon is 30. Hence, we round off 29 to the nearest 30.

So, we can say that round off off come the nearest 10 means that us wish to round turn off the last two digits of a number, i.e. Approximately the tens ar of a number.

From the over discussion, we have the right to see the there are two methods of round off off a number to the nearest 10. The two methods are –

Rounding UpRounding Down

Let us understand both techniques one by one.

## Rounding Up

If the number at the tens place is followed by 5, 6, 7, 8, or 9, the number is rounded up.

Example – We want to round off 5489 come the nearest 10.

Look because that the number at the ten’s place. It is 8.

3. Due to the fact that this number is much less than 5, us round down the number, i.e. We round it turn off to the nearest 10 that comes prior to this number. So, 1 i do not care 0 which by including to 6 in ~ the ten’s place, i do not care 60.

Hence, the number 2461 after gift rounded turn off to the nearest 10 is 2460.

Note: here we relocated down the number to the nearest ten, i beg your pardon is why it is referred to as rounding down.Let us consider another example

Example – We want to round off 473 to the nearest 10.

Look because that the digit at the ten’s place. It is 7.

3. Because this number is less than 5, us round down the number, i.e. Us round it turn off to the nearest 10 the comes before this number. So, 3 i do not care 0 i m sorry by adding to 7 in ~ the ten’s place, becomes 70.

Hence, the number 473 after being rounded off to the nearest 10 is 470.

## Graphical Representation

Rounding off to the nearest 10 can also be taken graphically as presented below

First, it have to be construed that once you space rounding turn off to the nearest 10, the number at the hundred’s ar needs to it is in looked into.

Let us take a number 74

This number lies between 70 and also 80. To round off this number, either us take it earlier to 70 or move it forward to 80. How do we decide where to go?

Look in ~ the number line below –

The numbers the lie in the red areas will certainly be rounded down to 70. Similarly, the numbers the lie in the blue areas will it is in rounded up to 80. This is because the numbers the lie in red areas, i.e. The numbers in between 71 and 74 room closer come 70 as contrasted to 80. For this reason they will certainly be rounded down.

However, the numbers that lie in between 75 and also 79 room closer come 80 because of which they would be rounded up to 80.

So, what are the rule for round off off a number come the nearest 10?

So, what space the steps affiliated in round off off a number come the nearest 10? permit us find out.

## Steps connected in rounding off a number to the nearest 10

The complying with steps are involved in round off off a number come the nearest 10 –

Obtain the number.Examine the digit at the one’s ar of the given number.If the number at the one’s place of the offered number is much less than 5, then change the ones digit by 0 and also keep the other digits that space to the left of the ten’s digit as they are.If the number at the one’s location of the given number is greater than or equal to 5, then replace the ones digit by 0 and increase the tens digit by 1 and also keep the various other digits that space to the left that the ten’s digit as they are. In instance the digit at the ten’s place include to 10, then keep the 0 in ~ the 10s place and carry the 1 at the hundreds ar and add it to the number at hundreds places, comparable to what you do in addition.The number so obtained is the number created by round off off a number come the nearest 10.

## Rules for round off off a number to the nearest 10

Based on what we have learnt above, we can say the there are two rule for round off off a number to the nearest 10. These two rules are –

While round off off to the nearest ten if the number in the units location is between 0 and 4 which means that the unit number is equal to 0 or is much less than or same to 4, climate the unit digit will certainly be changed by 0.If the digit in the unit location lies in between 5 and 9, which method that the unit number is better than or same to 5 yet is much less than or same to 9, then the units place is replaced by ‘0’ and also the tens place increased by 1.

So, we deserve to summarise it together –

We have learnt exactly how to round off whole numbers come the nearest 10. However what if we desire to round off a decimal number come the nearest 10? execute the same rules apply or execute we execute something different? permit us find out.

## Rounding off Decimal numbers to the nearest 10

There space no separate rules as soon as it comes to rounding off decimal numbers to the nearest 10. This method that irrespective of the number of digits after the decimal point in a decimal number, us round it off to the nearest 10 together we execute for a entirety number. Permit us understand it v an example.

Example

Suppose we want to round off the number 149.278 to the nearest 10. Exactly how will we perform it? let us find out.

Solution

Carefully observe the provided number 149.278. Which number is in ~ the ten’s place? The number is 4. Now, us look in ~ the number to the right of the digit at the ten’s place. The number is 9. We will go by the same dominion as we did for totality numbers.

Since this number is higher than 5, we round up the number, i.e. We round it off to the nearest 10 that comes beside this number. So, 9 becomes 10 i beg your pardon by adding to 4 at the ten’s place, becomes 50.

Hence, the number 149.278 after being rounded turn off to the nearest 10 is 71150.

Let us consider another example.

Example

Suppose we desire to round off the number 2153.189 to the nearest 10. How will we carry out it? permit us find out.

Solution

Carefully watch the given number 2153.189. Which number is at the ten’s place? The number is 5. Now, we look in ~ the number to the best of the number at the ten’s place. The number is 3. We will certainly go through the same rule as we did for totality numbers.

Since this number is less than 5, us round down the number, i.e. Us round it turn off to the nearest 10 that comes before this number. So, 3 i do not care 0 i m sorry by including to 5 in ~ the ten’s place, i do not care 50.

Hence, the number 2153.189 after gift rounded off to the nearest 10 is 2150.

## Solved Examples

Example 1 Round turn off the whole number 23 come the nearest 10

Solution We have been provided the entirety number 23 and also we need to round it off to the nearest 10. Let us see how to perform it based upon what we have learnt above.

Examine the number 23. Look because that the digit at the ten’s place. The number is 2. Currently look because that the number to the appropriate of the number at the ten’s place. The number is 3.

Since this number is much less than 5, we round down the number, i.e. We round it turn off to the nearest 10 the comes prior to this number. So, 3 i do not care 0 i beg your pardon by adding to 2 at the ten’s place, becomes 20.

Hence, the number 23 after gift rounded turn off to the nearest 10 is 20.

Graphically, we have the right to represent it as –

Example 2 Round off the whole number 57 to the nearest 10

Solution We have actually been provided the whole number 57 and we have to round it off to the nearest 10. Let united state see how to perform it based upon what we have actually learnt above.

Examine the number 57. Look because that the digit at the ten’s place. The number is 5. Currently look for the number to the best of the number at the ten’s place. The number is 7.

Since this number is greater than 5, us round up the number, i.e. Us round it turn off to the nearest 10 the comes next to this number. So, 7 becomes 10 which by adding to 5 in ~ the ten’s place, i do not care 60.

Hence, the number 57 after gift rounded off to the nearest 10 is 60.

Graphically, we can represent it together –

Example 3 Round off the totality number 364 come the nearest 10

Solution We have been provided the entirety number 364 and we should round it off to the nearest 10. Let united state see exactly how to perform it based upon what we have actually learnt above.

Examine the number 364. Look for the digit at the ten’s place. The number is 6. Currently look because that the number to the ideal of the digit at the ten’s place. The number is 4.

Since this number is less than 5, us round down the number, i.e. We round it off to the nearest 10 that comes before this number. So, 4 becomes 0 which by adding to 6 in ~ the ten’s place, becomes 60.

Hence, the number 364 after gift rounded off to the nearest 10 is 360.

Graphically, we can represent it as –

Example 4 Round turn off the numbers 458 and also 651 come the nearest 10. Find the amount of these numbers before rounding off also after it. Also, uncover the difference in between both the sums.

Solution We have been provided the numbers, 458 and also 651. We need to perform the adhering to –

Find the amount of 458 and 651 prior to rounding offRound turn off the number 458 and 651 come the nearest 10.Find the sum of 458 and 651 after round off offFind the difference between both the sums.

Let us perform them one by one.

First, permit us discover the sum of the provided numbers.

We have actually 458 + 651 = 1109 ……………………………… ( 1 )

Next, we shall round off the numbers 458 and also 651 to the nearest 10. We have,

Examine the number 651. Look for the number at the ten’s place. The number is 5. Now look for the digit to the ideal of the digit at the ten’s place. The number is 1.

Since this number is much less than 5, us round down the number, i.e. Us round it turn off to the nearest 10 the comes prior to this number. So, 1 i do not care 0 i m sorry on adding to52 in ~ the ten’s place, becomes 50.

Hence, the number 651 after being rounded off to the nearest 10 is 650.

Now, let united state round turn off 458 come the nearest 10.

Examine the number 458. Look because that the digit at the ten’s place. The number is 5. Now look because that the digit to the best of the number at the ten’s place. The number is 8.

Since this number is better than 5, us round up the number, i.e. Us round it off to the nearest 10 the comes beside this number. So, 8 i do not care 10 i m sorry by including to 5 in ~ the ten’s place, becomes 60.

Hence, the number 458 after gift rounded turn off to the nearest 10 is 460.

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So, we have,

651 round off to the nearest 10 = 650

458 round off to the nearest 10 = 460 ………………………………… ( 2 )

Let united state now find the sum of the numbers obtained after rounding off. Us have,

650 + 450 = 1100 ……………………. ( 3 )

Last, we discover the difference in between the sums derived before and also after round off off. Therefore, from ( 1 ) and also ( 3 ) we have,

1109 – 1100 = 9

Hence, the difference between the sums obtained before and after rounding off = 9

## Key Facts and Summary

When round off off a number come thenearest tens, look in ~ the ONES DIGITof the number.

Rounding turn off to the nearest 10 method that us wish come round turn off the last two digits that a number, i.e. Approximately the tens ar of a number.If the digit is 0, 1, 2, 3, or 4, girlfriend willround downto the ahead tens. (Round down)If the digit is 5, 6, 7, 8, or 9, girlfriend willround upto the following ten. (Round Up)

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