+0  
 
+2
122
3
avatar+344 

https://vle.mathswatch.co.uk/images/questions/question1470.png

 

smileysmileysmiley

qualitystreet  Feb 13, 2018
 #1
avatar
+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
avatar+87572 
+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

 

 

cool cool cool

CPhill  Feb 13, 2018
 #3
avatar+344 
0

Thanks both of you for helping.

 

smileysmileysmiley

qualitystreet  Feb 14, 2018

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