CONVERSION OF COMMON FRACTION INTO DECIMAL FRACTION -
Method 1)-
To change a common fraction into a decimal fraction, we first change the given common fraction into an equivalent common fraction whose denominator is 10 or a multiple of 10. After that we change it into a decimal fraction.
To convert the fraction whose denominator is 10 or a multiple of 10 into a decimal fraction we follow the following steps:
1) Count the zeros in the denominator.
2) Write the numerator in the answer, then add the decimal point to the numerator. The number of digits on the right of the decimal point is equal to the number of zeros in the denominator. So we will count the digits from the right to the left while putting the decimal point, and the final result will represent the answer.
Q) Convert the following common fractions into decimal fractions:
5 3
i) ------ ii) 5 ------
8 4
5 5 × 125 625
i) ------- = ------------ = ------- = 0.625 (Ans.)
8 8 × 125 1000
[Multiply denominator 8 by 125, we get the denominator 10 or multiplication of 10. So now we can convert fraction into decimal]
3 (5 × 4) + 3 23 23 × 25
ii) 5 ------ = ------------- = ------- = ------------
4 4 4 4 × 25
[Multiply denominator 25 by 4, we get the denominator 10 or multiplication of 10. So now we can convert fraction into decimal]
575
= -------- = 5.75 (Ans.)
100
3 (20 × 5) + 3 103 103 X 2
iii) 20 ------ = -------------- = ------- = -----------
5 5 5 5 X 2
[Multiply denominator 5 by 2, we get the denominator 10 or multiplication of 10. So now we can convert fraction into decimal]
206
= ------- = 20.6 (Ans.)
10
Method 2)-
We can also adopt the following division method to change a common fraction into a decimal fraction.
Use the following steps :-
1) We divide the numerator by the denominator.
2) When a non-zero remainder is left, we insert a decimal point in the dividend and the quotient and put a zero on the right of the decimal point in the dividend and the remainder. Divide again.
3) We continue the division process just as in the case of whole numbers till the remainder is zero.
5
Example.1) --------
4
Ans.) 4 ) 5 ( 1.25
4
---------
10
8
--------
20
20
-------
0
so, the required answer is 1.25 (Ans.)
3
Example.2) 5 ------
8
Ans.) First convert mix fraction to improper fraction, and we get -
1 (5 X 8) + 1 41
5 ------- = ------------- = ------
8 8 8
8 ) 41 ( 5.125
40
---------
10
8
--------
20
16
--------
40
40
--------
0
So, the desired result is 5.125 (Ans.)