## What Do You Mean by Rounding Off a Number?

Rounding off is nothing but estimation. Estimating the actual number to its nearby number is called rounding off.

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## Example of Rounding Off from Everyday Life!

When someone asks you the price of your book, you say 100 even if it is 98. This is giving an estimation after rounding off a number. This is how we apply the concept of rounding off in our everyday life.

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## How to Round Off Different Numbers?

Different numbers use different ‘rounding off’ rules. Let’s discuss them one by one.

### Whole Numbers

Whole numbers are rounded off at different place values.

#### Nearest Ten

Check the unit place digit:

- If the unit place digit is less than 5 then keep the tens place digit the same and put 0 at the unit place.
- If the unit place is 5 or more than 5 then change the tens digit into its successor and put 0 at the unit place.

#### Example:

If we round off 15,493 to the nearest tens place then the answer will be 15,490.

As the unit place is less than 5, the tens place digit will not change.

Similarly, if we round off 12,359 to its nearest tens place then the answer will be 12,360.

As the unit place is more than 5, the tens place digit will change its successor.

#### Nearest Hundred

Check the tens place digit:

- If the tens place is less than 5 then keep the hundred place digit the same and put 0 at the tens and unit place.
- If the tens place is 5 or more than 5 then change the hundred digit into its successor and put 0 at the tens and unit place.

#### Example:

If we round off 15,443 to the nearest hundred places then the answer will be 15,400. As the tens place is less than 5, the hundred place digit will not change.

Similarly, if we round off 12,359 to its nearest hundred places then the answer will be 12,400.

As the tens place is 5, the hundred place digit will change to its successor.

#### Nearest Thousand

Check the hundred place digit:

- If the hundred place digit is less than 5 then keep the thousand place digit the same and put 0 at the hundred, tens, and unit place.
- If the hundred place digit is 5 or more than 5 then change the thousand place digit into its successor and put 0 at the hundred, tens, and unit place.

#### Example:

If we round off 15,443 to the nearest thousand place digit then the answer will be 15,000. As the hundred place digit is less than 5, the thousand place digit will not change.

Similarly, if we round off 12,659 to its nearest thousand place digit then the answer will be 13,000.

As the hundred place digit is more than 5, the thousand place digit will change to its successor.

### Decimal Number

The concept is quite similar to the whole number with some minor but noteworthy changes. If the digit right to the place value you are rounding to is less than 5, round down. However, if it’s 5 or more than 5, round up.

#### Nearest Whole

5.9165 rounded to the **nearest whole** is 6.

As 5 is followed by 9 and 9 is greater than 5. So, round up.

#### Nearest Tenth

5.9165 rounded to the **nearest tenth** is 5.9

As 9 is followed by 1 and 1 is smaller than 5. So, round down.

#### Nearest Hundredth

5.9165 rounded to the **nearest hundredth** is 5.92.

As 1 is followed by 6 and 6 is greater than 5. So, round up.

#### Nearest thousandth

5.9165 rounded to the **nearest thousandth** is 5.917.

As 6 is followed by 5. So, round up.

## Solved Examples

**Example 1.**** **Round off the following numbers to the nearest ten:

- 5499
- 3,453
- 4,405

**Solution 1. **

- 5,499 rounded to the nearest ten is 5,500.

The unit place digit is more than 5 so add one to the tens place digit.

- 3,453 rounded to the nearest ten is 3,450.

The unit place digit is less than 5 so the tens place digit will remain the same.

- 4,405 rounded to the nearest ten is 4,410.

The unit place digit is 5 so add one to the tens place digit.

**Example 2. **Round off the following numbers to the nearest hundredth.

- 2.656
- 2.305
- 3.234

**Solution 2. **

- 2.656 rounded to the nearest hundredth is 2.66.

The digit next to the hundredth place digit is more than 5 so add 1 to the hundredth place digit.

- 2.305 rounded to the nearest hundredth is 2.31.

The digit next to the hundredth place digit is 5 so add 1 to the hundredth place digit.

- 3.234 rounded to the nearest hundredth is 3.23.

The digit next to the hundredth place digit is less than 5 so the hundredth place digit will remain the same.

**Example 3.**Round off the following numbers to the nearest thousand.

- 44,590
- 66,235

**Solution 3.**

- 44,590 rounded to the nearest thousand is 45,000.

The hundred place digit is 5 so add 1 to the thousand place digit.

- 66,235 rounded to the nearest thousand is 66,000.

The hundred place digit is less than 5 so keep the thousand place digit the same as before.

## Practice Problems

## Rounding off

### A number rounded to the nearest 10 is 500. What could be the possible number?

495 will be rounded off to 500.

### Simplify the following after rounding off each number to the nearest hundred

45,789 + 23,848 + 66,321 – 34,213

45,800 + 23,800 + 66,300 – 34,200 = 101,700

### Match the numbers with their round off to the nearest tens.

4,509 will round to 4,510.

**98,683 will round to 98,680.**

**21,498 will round to 21,500.**## Frequently Asked Questions

Can we round off lengths and heights?

Yes. Heights and lengths can be rounded off.

What is 9,999 rounded off to the nearest hundred?

If we round off 9,999 to the nearest hundred, we will get 10,000.

Are round-off figures exact?

No. Round-off figures are not exact but are in proximity to the exact figure.