Chapter 5: Q53. (page 225)

Write the decimal as a fraction or mixed number.
$0 . \bar{12}$

Short Answer

Expert verified

The fraction is $\frac{4}{33}$ .

Step by step solution

Step 1. Given information

Consider, the decimal $0 . \bar{12}$ provided in question.

Step 2. Calculation

Let $x = 0 \cdot \bar{12}$

$x = 0 \cdot 121212 . . . . .$ …… (1)

Clearly, 12 is the only digit which is repeating in equation (1)

Multiply equation (1) by 100 on both sides

$100 x = 12 \cdot 1212 . . . . .$ …… (2)

Subtract equation (1) from equation (2),

Therefore,

$\begin{matrix} 100 x - x = (12 \cdot 1212.....) - (0 \cdot 121212.....) \\ 99 x = 12 \\ x = \frac{12}{99} \\ x = \frac{4}{33} \end{matrix}$

Thus, the fraction number that can be formed is $\frac{4}{33}$ .

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Write the decimal as a fraction or mixed number.
$0 . \bar{12}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Write the decimal as a fraction or mixed number.0.12¯

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Calculus

Logic and Functions

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Write the decimal as a fraction or mixed number.
$0 . \bar{12}$