Question

If the recurring decimal 0.84181 (underline on 81)be written as a fraction in its lowest terms, the different between the denominator and the numerator is?

Answer 1

Solution:-

In 0.84181 (underline on 81)
It means 81 is the recurring number.
⇒ 84181 - 841
Now put denominators with '9' as many times as the length of the recurring number, i.e. there are 2 digits in 81
So,
(84181 - 841)/99000
= 83340/99000
= 8334/9900
Taking the H.C.F. of these two numbers by long division method.
H.C.F. of 8334 and 9900 is 18
(8334÷18)/(9900÷18)
= 463/550
Difference between the denominator and numerator is 
= 550 - 463
= 87
Answer.