Question

0.5(repeated)+0.1(repeated)-0.3(repeated)?

Answer 1

`(1)/(3)=0.\overline{3}`

Explanation:

Since a single digit is repeated in each case, and since the repeat starts at the decimal point, the fraction corresponding to the repeated digit is that digit divided by 9.

`0.\overline{5}+0.\overline{1}-0.\overline{3}=(5)/(9)+(1)/(9)-(3)/(9)=(5+1-3)/(9)=(3)/(9)\\\\=\boxed{(1)/(3)}`

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Comment on equivalents to repeating decimals

The number of 9s in the denominator equals the number of repeated digits.

0.2727(repeated) = 27/99 = 3/11 . . . . . 2 repeated digits