Question

express the following in the form of p/q where p and q are integers and q not equal to zero. 0.4747474747.........

Answer 1

0.47 ( bar on 47 ).


Let X = 0.47


Then , X = 0.4747 -----------(1)



multiplying equation (1) by 100 , we get


100X = 47.4747 ------------(2)



Subtracting equation (1) from equation (2) , we get


100X = 47.4747

X = 0.4747
-----------------------


99X = 47


X = 47/99 [ P/Q form ]


Hence,

0.47 ( bar on 47 ) is of the form 47/99 , which is in the form of P/Q.

Answer 2

$<b>$Your answer !!

$let \: x = 0.47474747..... ( \alpha )\\ \\ = > 100x = 47.47474747..... ( \beta )\\ \\ subtract ( \alpha )from( \beta ) \\ \\ = > 100x - x = 47.47474747 - 0.47474747\\ \\ = > 99x = 47 \\ \\ = > x = \frac{47}{99}$

Thanks !!