Question

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

Answer 1

Answer:

  $\dfrac{1}{3}=0.\overline{3}$

Step-by-step 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.

  $0.\overline{5}+0.\overline{1}-0.\overline{3}=\dfrac{5}{9}+\dfrac{1}{9}-\dfrac{3}{9}=\dfrac{5+1-3}{9}=\dfrac{3}{9}\\\\=\boxed{\dfrac{1}{3}}$

_____

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