**Introduction**

Numbers are very commonly used in our day to day life. In general, we need not state the exact number as an answer to the question which requires us to tell about how many. In other words, in order to ease our calculations, we often approximate the numbers to some extent. It helps us give approximate answers where exact values are not required. For instance, we may say that there are around 600 students in a school. That does not necessarily mean that there are exactly 600 students in a school. The exact number of students in the school may be somewhere around 600 which, for convenience, we have rounded off to 600. Rounding off is also termed as a shortcut method. Another example can be if you plan an event at home you can just estimate the number of guests that are supposed to attend the event. It can be a rough estimate of the number of people say 200. This does not mean that exactly 200 people will attend the event. This means we can round off numbers to the nearest place value, say 10, 100, 1000 etc.

Let us learn what we mean by rounding off to the nearest 10. Let us find out.

**How do we round off a number to the nearest 10?**

Consider two numbers 22 and 29. If we plot these numbers on a number line we find that both 22 and 29 lies between 20 and 30. Also, 22 is nearer to 20 while 29 is nearer to 30. So, we round off 22 to 20. Correct to the nearest tens. If we consider 29, we round off it to the nearest 10 which is 30. Hence, we round off 29 to the nearest 30.

**So, we can say that rounding off to the nearest 10 means that we wish to round off the last two digits of a number, i.e. up to the tens place of a number.**

From the above discussion, we can see that there are two ways of rounding off a number to the nearest 10. The two methods are –

- Rounding Up
- Rounding Down

Let us understand both methods 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 to the nearest 10.**

- Look for the digit at the ten’s place. It is 8.

- Now look for the digit to the right of the digit at the ten’s place. The number is 9

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 9 becomes 10 which by adding to 8 at the ten’s place, becomes 90.

Hence, the number 5489 after being rounded off to the nearest 10 is **5490**

Note: Here we moved up the number to the nearest ten, which is why it is called rounding up.

**Let us take another example. **

**Example – We want to round off 7136 to the nearest 10.**

- Look for the digit at the ten’s place. It is
**3**.

- Now look for the digit to the right of the digit at the ten’s place. The number is
**6**

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 7 becomes 10 which by adding to 6 at the ten’s place, becomes 70.

Hence, the number 7136 after being rounded off to the nearest 10 is **71400**

Now that we have understood what we mean by rounding up, let us understand what is meant by rounding down.

**Rounding Down**

**If the number at the hundred’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. **

**Example – We want to round off 2461 to the nearest 10.**

- Look for the digit at the ten’s place. It is
**6**.

2. Now look for the digit to the right of the digit at the ten’s place. The number is **1****.**

3. Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which by adding to 6 at the ten’s place, becomes 60.

Hence, the number 2461 after being rounded off to the nearest 10 is **2460****.**

Note: Here we moved down the number to the nearest ten, which is why it is called rounding down.

**Let us consider another example**

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

- Look for the digit at the ten’s place. It is 7.

2. Now look for the digit to the right of the digit at the ten’s place. The number is **3****.**

3. Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 3 becomes 0 which by adding to 7 at 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 understood graphically as shown below**

First, it should be understood that when you are rounding off to the nearest 10, the digit at the hundred’s place needs to be looked into.

**Let us take a number 74**

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

**Look at the number line below – **

The numbers that lie in the **red areas** will be rounded down to 70. Similarly, the numbers that lie in the blue areas will be rounded up to 80. This is because the numbers that lie in red areas, i.e. the numbers between 71 and 74 are closer to 70 as compared to 80. Hence they will be rounded down.

However, the numbers that lie between 75 and 79 are closer to 80 due to which they would be rounded up to 80.

So, what are the rules for rounding off a number to the nearest 10?

So, what are the steps involved in rounding off a number to the nearest 10? Let us find out.

**Steps Involved in Rounding off a number to the nearest 10**

The following steps are involved in rounding off a number to the nearest 10 –

- Obtain the number.
- Examine the digit at the one’s place of the given number.
- If the digit at the one’s place of the given number is less than 5, then replace the ones digit by 0 and keep the other digits that are to the left of the ten’s digit as they are.
- If the digit at the one’s place 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 keep the other digits that are to the left of the ten’s digit as they are. In case the digit at the ten’s place add to 10, then keep the 0 at the tens place and carry the 1 at the hundreds place and add it to the digit at hundreds places, similar to what you do in addition.
- The number so obtained is the number formed by rounding off a number to the nearest 10.

**Rules for Rounding off a number to the nearest 10**

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

- While rounding off to the nearest ten if the digit in the units place is between 0 and 4 which means that the unit digit is equal to 0 or is less than or equal to 4, then the unit digit will be replaced by 0.
- If the digit in the unit place lies between 5 and 9, which means that the unit digit is greater than or equal to 5 but is less than or equal to 9, then the units place is replaced by ‘0’ and the tens place increased by 1.

So, we can summarise it as –

We have learnt how to round off whole numbers to the nearest 10. But what if we want to round off a decimal number to the nearest 10? Do the same rules apply or do we do something different? Let us find out.

**Rounding off Decimal Numbers to the nearest 10**

There are no separate rules when it comes to rounding off decimal numbers to the nearest 10. This means that irrespective of the number of digits after the decimal point in a decimal number, we round it off to the nearest 10 as we do for a whole number. Let us understand it with an example.

**Example**

Suppose we want to round off the number 149.278 to the nearest 10. How will we do it? Let us find out.

**Solution**

Carefully observe the given number 149.278. Which number is at the ten’s place? The number is 4. Now, we look at the digit to the right of the digit at the ten’s place. The number is 9. We will go by the same rule as we did for whole numbers.

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 9 becomes 10 which by adding to 4 at the ten’s place, becomes 50.

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

Let us consider another example.

**Example**

Suppose we want to round off the number 2153.189 to the nearest 10. How will we do it? Let us find out.

**Solution**

Carefully observe the given number 2153.189. Which number is at the ten’s place? The number is 5. Now, we look at the digit to the right of the digit at the ten’s place. The number is 3. We will go by the same rule as we did for whole numbers.

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 3 becomes 0 which by adding to 5 at the ten’s place, becomes 50.

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

**Solved Examples**

**Example 1** Round off the whole number 23 to the nearest 10

**Solution** We have been given the whole number 23 and we need to round it off to the nearest 10. Let us see how to do it based on what we have learnt above.

Examine the number 23. Look for the digit at the ten’s place. The number is 2. Now look for the digit to the right of the digit at the ten’s place. The number is **3****.**

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 3 becomes 0 which by adding to 2 at the ten’s place, becomes 20.

Hence, the number 23 after being rounded off to the nearest 10 is **20.**

Graphically, we can represent it as –

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

**Solution** We have been given the whole number 57 and we need to round it off to the nearest 10. Let us see how to do it based on what we have learnt above.

Examine the number 57. Look for the digit at the ten’s place. The number is 5. Now look for the digit to the right of the digit at the ten’s place. The number is **7.**

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 7 becomes 10 which by adding to 5 at the ten’s place, becomes 60.

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

Graphically, we can represent it as –

**Example 3** Round off the whole number 364 to the nearest 10

Solution We have been given the whole number 364 and we need to round it off to the nearest 10. Let us see how to do it based on what we have learnt above.

Examine the number 364. Look for the digit at the ten’s place. The number is 6. Now look for the digit to the right of the digit at the ten’s place. The number is 4**.**

Since this number is less than 5, we 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 at the ten’s place, becomes 60.

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

Graphically, we can represent it as –

**Example 4** Round off the numbers 458 and 651 to the nearest 10. Find the sum of these numbers before rounding off as well after it. Also, find the difference between both the sums.

**Solution** We have been given the numbers, 458 and 651. We need to perform the following –

- Find the sum of 458 and 651 before rounding off
- Round off the numbers 458 and 651 to the nearest 10.
- Find the sum of 458 and 651 after rounding off
- Find the difference between both the sums.

Let us do them one by one.

First, let us find the sum of the given numbers.

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

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

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

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which on adding to52 at the ten’s place, becomes 50.

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

Now, let us round off 458 to the nearest 10.

Examine the number 458. Look for the digit at the ten’s place. The number is 5. Now look for the digit to the right of the digit at the ten’s place. The number is **8.**

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 8 becomes 10 which by adding to 5 at the ten’s place, becomes 60.

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

So, we have,

651 round off to the nearest 10 = 650

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

Let us now find the sum of the numbers obtained after rounding off. We have,

650 + 450 = 1100 ……………………. ( 3 )

Last, we find the difference between the sums obtained before and after rounding off. Therefore, from ( 1 ) and ( 3 ) we have,

1109 – 1100 = 9

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

**Key Facts and Summary**

When rounding off a number to the nearest tens, look at the **ONES DIGIT** of the number.

- Rounding off to the nearest 10 means that we wish to round off the last two digits of a number, i.e. up to the tens place of a number.
- If that digit is 0, 1, 2, 3, or 4, you will round down to the previous tens. (Round down)
- If that digit is 5, 6, 7, 8, or 9, you will round up to the next ten. (Round Up)

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