#1**+2 **

0.14242424242........etc. Take the reciprocal of it:

7.021276595744680851063829787234 - 7 Take the reciprocal of the fraction:

47 - This is the numerator.

47 x 7.021276595744680851063829787234

330 - This is the denominator: So the fraction is:

**47 / 330**

Guest Feb 13, 2018

#2**+1 **

Here's my method, QS

Forget the decimal and write the non-repeating and repeating parts ⇒ 142

(1) Subtract the non-repeating part from this = 142 - 1 = 141

(2) Write this over an integer that has the same number of leading 9's as digits in the the repeating part and the same number of 0's as digits in the non-repeating part ⇒ 990

So we have

141 / 990 = 47 / 330

CPhill
Feb 13, 2018