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Riya wrote $0. \overline{5} = \frac{5}{10}$ . What is the correct fraction?

Class 9Decimal Expansions of Real NumbersNumber Systems

A $\frac{5}{99}$
B $\frac{1}{2}$
C $\frac{5}{9}$
D $\frac{55}{100}$

Step-by-Step Solution

x = 0.555

…,

10 x = 5.555

…, so

9 x = 5

and

x = 5/9

. Riya's 5/10 = 0.5 stops after one digit.

Answer: C)

\frac{5}{9}

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