untitled

Required fraction is
1665

224

5

Example 8. Express 42. 347  8  into simple fraction.

Solution: 42. 347  8  = 42. 347878 ........
So, 42. 347  8 u 10000 42. 347878 .........u 10000 42348. 7878

and 42. 347  8 u 100 = 42. 347878 ........u 100 = 4234. 7878

Subtracting, 42. 347  8  u 9900 = 423478  4234

Therefore, 42. 347  8 =
825

287

825 42

34937

9900

419244

9900

423478 4234



Required fraction is
825

287

42

Explanation : From the examples 5, 6, 7 and 8 , it appears that,

x The recurring decimal has been multiplied by the number formed by putting at the
right side of 1 the number of zeros equal to the number of digits in the right side of
decimal point in the recurring decimal.

x The recurring decimal has been multiplied by the number formed by putting at the
right side of 1 the number of zeros equal to the number of digits which are non-
recurring after decimal point of the recurring decimal.

x the second product has been subtracted from the first product. By subtracting the
second product from the first product the whole number has been obtained at the
right side. Here it is observed that, the number of non-recurring part has been
subtracted from the number obtained by removing the decimal and recurring points
of recurring decimal fraction.

x The result of subtraction has been divided by the number formed by writing the same
number of 9 equal to the number of digits of recurring part at the left and number of
zeros equal to the number of digits of non-recurring part at the right.

x In the recurring decimals, converting into fractions the denominator is the number of
9 equal to the number of digits in the rec urring part and in right side of all 9’s
number of zeros equal to the number of digits in the non-recurring part. And the
numerator in the result that is obtained by subtracting the number of the digits
formed by omitting the digits of recurring part from the number formed by removing
the decimal and recurring points of recurring decimal.

Remark : Any recurring decimal can also be converted into a fraction. All recurring
decimals are rational numbers.

Example 9. Express 5. 234  57  into simple fraction.