# Division of Decimal Numbers

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Savita was preparing a design to decorate her classroom. She needed a few coloured strips of paper of length 1.9 cm each. She had a strip of coloured paper of length 9.5 cm. How many pieces of the required length will she get out of this strip? She thought it would be

Both 9.5 and 1.9 are decimal numbers. So we need to know the division of decimal numbers too!

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## Division by 10, 100 and 1000

Let us see if we can find a pattern for dividing numbers by 10, 100 or 1000. This may help us in dividing numbers by 10, 100 or 1000 in a shorter way.

1 | 2 | 3 |
---|---|---|

31.5 ÷ 10 = | 231.5 ÷ 10 = | 1.5 ÷ 10 = |

31.5 ÷ 100 = | 231.5 ÷ 100 = | 1.5 ÷ 100 = |

31.5 ÷1000 = | 231.5 ÷ 1000 = | 1.5 ÷ 1000 = |

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In 31.5 and 3.15, the digits are same i.e., 3, 1, and 5 but the decimal point has shifted in the quotient. To which side?

The decimal point has shifted to the left by one place. Note that 10 has one zero over

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## Division of a Decimal Number by a Whole Number

**(i) Let us find **

- Writing the fraction form we get: 6.4 =
and 2 = - So, 6.4 ÷ 2 can be re-written as
- Taking the reciprocal and evaluating we get
6.4 ÷ 2 = - Simplifying
- Hence we have found the answer.

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**(ii) Let us find 12.96 ÷ 4**

- Writing the fraction form we get: 12.96 =
and 4 = - So, 12.96 ÷ 4 can be re-written as
- Taking the reciprocal and evaluating we get
12.96 ÷ 4 = - Simplifying
- Hence we have found the answer.

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Note that here and in the next section, we have considered only those divisions in which, ignoring the decimal, the number would be completely divisible by another number to give remainder zero. Like, in 19.5 ÷ 5, the number 195 when divided by 5, leaves remainder zero.

However, there are situations in which the number may not be completely divisible by another number, i.e., we may not get remainder zero. For example, 195 ÷ 7. We deal with such situations in later classes.

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## Division of a Decimal Number by another Decimal Number

**(i)Let us find **

- Writing the fraction form we get: 25.5 =
and 0.5 = - So,
25.5 ÷ 0.5 can be re-written as - Taking the reciprocal and evaluating we get
25.5 ÷ 0.5 = - Simplifying
- Hence we have found the answer.

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What do you observe? For

Or, we say the decimal point was shifted by one place to the right in 0.5 to make it 5. So, there was a shift of one decimal point to the right in 25.5 also to make it 255.

## Example 6

**Each side of a regular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5cm. How many sides does the polygon have?**

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## Example 7

**A car covers a distance of 89.1 km in 2.2 hours. What is the average distance covered by it in 1 hour?**