When dividing one number by another we frequently obtain more numbers than the original one. To take an extreme example, if we divide two by six, the resulting number is 0.33333 recurring. When this happens one will have question in there mind how do we go about rounding the decimals. If restricted ourselves to having two more digit than the original number, then dividing 2 by 6 would become 0.33. In this section we will be learning more about rounding numbers.

## Rules For Rounding Numbers

The standard rule for rounding a number is to round down when the fractional or decimal part is less than half, round up when the fraction part is more than half, and round to the closer even number when the fractional part is exactly half.

## Rounding with Number Lines

Here we are going to learn how to round up the numbers using number line. Basically we have to round up the decimal values to the nearest value. To round the number, draw a number line and mark the value in the number line. One can very easily find the halfway point by folding the number line. If the number falls to the left of the halfway point, round down. If the number falls to the right of the halfway point, round up.
Example: Round the value $\frac{7}{9}$ using number line

Solution: The decimal value of given rational number

$\frac{8}{9}$ = $0.888$

Mark this value into the given number line

From this number line we can see that $0.888 \cong 1$

## How to Round off Numbers

The steps for rounding numbers to the nearest whole number or to the nearest decimal place:

1) If the final number is 5 or above, round up to the next tens place.

2) If the number is less than 5, round down to the last tens.

Example:

0.844 round down to 0.84

4.325 round up to 4.33

0.33 round down to 0.3

2.39
round up to 2.4

3) To get the result which is rounded off to the nearest 10th, look at the numbers in the 100th place and follow the above rule

4) To get the result which is rounded off to the nearest 100th, look at the numbers in the 1000th place and follow the above rule

5) To get the result which is rounded off to the nearest 1000th, look at the numbers in the 10000th place and follow the above rule

## Examples of Rounding Numbers

The following are the example for Rounding numbers:

Example 1: Round the following number to nearest 10th position.

a) 0.12
b) 0.668

Solution:
a) 0.12 round down to 0.1
b) 0.668 round up to 0.7

Example 2: Round the following number to nearest 100th position.

a) 0.663
b) 2.375

Solution:
0.663 round down to 0.66
2.375 round up to 2.38

Example 3: Round the following number to nearest 100th position.

a) 1.3758
b) 0.0023

Solution:
1.3758 round up to 1.376
0.0023 round down to 0.002