In this chapter we will learn the meaning of rounding decimals and different methods to round off decimals.

## What is rounding off decimals?

Sometime the value of a decimal is so large that it becomes a pain to write it again and again.

For Example, consider the below number;

Writing such a long number will take up long time and create frustration.

So instead of writing the full numbers, we put the approximate value of the number which is closer to the original number.

See that the above number has been rounded off to two decimal places.

Using the approximate value 29.27 will have no affect in math problem as it is very close to the original number.

**Conclusion**

Rounding off decimals is finding the approximate value of the decimal number which is very close to the original number.

## How to Round off decimals

There are many ways to round off decimal numbers.

Usually while choosing the rounding off method there is a trade off between complexity and accuracy.

The method which makes the number less complex also makes it less accurate.

Here we will discuss** three methods**;

(a) Rounding off to whole number

(b) Rounding off to nearest tenth

(c) Rounding off to nearest hundredth

### Roundin**g off to whole number**

Here we** remove all the decimal points** and **select the number which is closest to the original value**.

This method makes the number less complex but the accuracy of number is also impacted the most.

**Follow the below steps** to round off decimal to whole number

Suppose the given decimal is **27.3827831**

**(a) Check the number just beyond the rounding number.**

Since we are rounding off to whole number, we will check the tenth place of decimal.

(**b) If Tenth Place = 0,1, 2, 3, 4.**

We will write the same whole number.

**If tenth place = 5, 6, 7, 8, 9.**

We will round up the whole number by 1.

Here the tenth place is 3.

So number 27 is the round off number.

Let us see some more examples;**Example 01**

Round off the decimal to nearest whole

257. 8678452

**Solution****(a) Check the tenth place of decimal**

**(b) Tenth Place = 8**

We will round up the whole number.

Hence, **258 is the round off number**.

**Example 02**

Round off decimal to nearest whole

650.58436

**Solution****(a) Check the tenth place of decimal**

**(b) Tenth place = 5**

We will round up the whole number.

Hence,** 651 is the solution**.

**Note**:

When we round up to whole number, the number will get less complex (with no decimal points) but the number is not that accurate.

### Rounding off to nearest tenth

Here we** round off the decimal number to 1 decimal place** (i.e. tenth place)

To round off the number, follow the below steps;

Let the number given is** 763.59732**.

**(a) Check the number after the tenth place**.

Since we are rounding off till tenth place we will check the number in hundredth place.

Here number 9 is in hundredth place.

**(b) If hundredth Place = 0,1, 2, 3, 4**.

We will write the same tenth number.

**If hundredth place = 5, 6, 7, 8, 9**.

We will round up the tenth number by 1.

Here the hundredth place number is 9.**So 763.6 is the roundoff number**.

Let us see some solved examples for our understanding.

**Example 01**

Round off decimal to nearest tenth **4.356721**

**Solution(a) Check the number in hundredth place**

**(b) Hundredth place = 5**

We will round up the number in tenth place.

Hence, **4.4 is the round off number**.

**Example 02**

Round off the below decimal to nearest tenth**95.637692**

**Solution****(a) Check the number in hundredth place**

**(b) Number in Hundredth place = 3**

There will be no change in value of tenth place.**Hence, 95.6 is the roundoff number**.

### Rounding off to nearest Hundredth

In this method we **round off number to two decimal place **( i.e. till hundredth place value).

To round off the number, do the following steps;

Let the given number be **783.675466**

**(i) Check the number next to hundredth place.**

Since we are rounding off number to hundredth place, we will check the number located next to it (i.e. in thousandth place)

Here the **number 5 lies in thousandth place**.

**(ii) If Thousandth Place = 0,1, 2, 3, 4.**

We will write the same hundredth number.

**If Thousandth place = 5, 6, 7, 8, 9.**

We will round up the hundredth number by 1.

Here the thousandth place number is 5.

So **783.68 is the roundoff number**.

Let us see some solved examples for our understanding.

**Example 01**

Round of the number to hundredth place

150.63789

**Solution****(a) Check the number in thousandth place**.

**(b) Here number in thousandth place = 7**

We will round up the number in hundredth place.

Number **150.64** is the round off number.

**Example 02**

Round of number to hundredth place**66.538106**

**Solution****(a) Check the number in thousandth place**

**(b) Number in Thousandth Place = 8**

We will round up number in hundredth place.

Hence, **66.54** is the required number.