Repeating decimal, part 2A

Number Theory Level 3

$0.\overline{123456790}=0.123456790123456790\ldots =\frac{a}{b}$

Given that $a$ and $b$ are coprime, find the value of $a+b$ .

Note : the repeated digits are without 8 , the period is 9.

1 solution

Chan Lye Lee
Dec 29, 2015

Let $x=0.\overline{123456790}=\frac{123456790}{999999999}$ .

Note that $12345679\times 81=999999999$ and hence $x=\frac{10}{81}$ . So $a+b=10+81=91$ .