Chapter 5: Q65. (page 226)

Write the decimal $0.3 \bar{21}$ as a fraction.

Short Answer

Expert verified

The fraction number of $0.3 \bar{21}$ is $\frac{53}{165}$ .

Step by step solution

Step 1. Given information

The decimal number is $0.3 \bar{21}$ .

Step 2. Calculation

Let x be $0.3 \bar{21}$ .

$x = 0.3212121$ …… (1)

Clearly, 21 is the only digit which is repeating in equation (1)

Multiply equation (1) by 10 on both sides,

$10 x = 3 . \bar{21}$

Consider, $3 . \bar{21} = 3 + 0 . \bar{21}$ but $0 . \bar{21} = \frac{21}{99}$ .

$\begin{matrix} 3 . \bar{21} = 3 + \frac{21}{99} \\ = \frac{(3 \times 99) + 21}{99} \\ = \frac{297 + 21}{99} \\ = \frac{318}{99} \end{matrix}$

Therefore,

$\begin{matrix} 10 x = \frac{318}{99} \\ x = \frac{318}{990} \\ = \frac{53}{165} \end{matrix}$

Thus, the fraction number that can be formed is $\frac{53}{165}$ .

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Write the decimal $0.3 \bar{21}$ as a fraction.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Write the decimal $0.3 \bar{21}$ as a fraction.