Division of Decimal Numbers
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
So we need to know the division of decimal numbers too!
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 = |
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
While dividing a number by 10, 100 or 1000, the digits of the number and the quotient are
Find:
(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.
(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.
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 a remainder of
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.
Find the average of 4.2, 3.8 and 7.6
Solution:
The average of 4.2, 3.8 and 7.6 =
(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.
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
So, there was a shift of one decimal point to the right in 25.5 also to make it
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