Write the recurring decimal 0.aaaaaa as a fraction.

Question

Write the recurring decimal 0.aaaaaa… as a fraction.

A
B
C
D

Answer 1

0.aaaaaaa... = 0.a + 0.0a + 0.00a + 0.000a + ...

This is a geometric series with common ratio r = 0.1

The sum of the series = [first term] / [1 - common ratio] = 0.a / 0.9 = a / 9

Answer 2

The fraction is a/(10¹ - 1) = a/9, so C.

aa/99 might be tempting as well, but this is saying a²/99, which is not equivalent to a/9