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Change $0.2 \overline{35}$ , where only 35 repeats, into a fraction.

Class 9Decimal Expansions of Real NumbersNumber Systems

A $\frac{233}{999}$
B $\frac{235}{990}$
C $\frac{233}{990}$
D $\frac{235}{999}$

Step-by-Step Solution

x = 0.23535

….

10 x = 2.3535

… and

1000 x = 235.3535

…. Subtract:

990 x = 233

, so

x = 233/990

.

Answer: C)

\frac{233}{990}

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