Chapter 5: Q75. (page 226)

Write $0 . \bar{475}$ as a fraction. Describe the steps you take to write the fraction.

Short Answer

Expert verified

The fraction number of $0 . \bar{475}$ is $\frac{475}{999}$ .

Step by step solution

Step 1. Given information

The decimal number is $0 . \bar{475}$ .

Step 2. Calculation

Let $x = 0 . \bar{475}$

$x = 0.475475475$ …… (1)

Clearly, 4 is the only digit which is repeating in equation (1)

Multiply equation (1) by 1000 on both sides,

$1000 x = 475.475475 . . . . .$ …… (2)

Subtract equation (1) from equation (2),

$(1000 x = 475 . 475475...) - (x = 0 . 475475...)$

$\begin{matrix} 1000 x - x = (475 . 475475.....) + (0 . 475475475.....) \\ 999 x = 475 \\ x = \frac{475}{999} \end{matrix}$

Thus, the fraction number that can be formed is $\frac{475}{999}$ .

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Write $0 . \bar{475}$ as a fraction. Describe the steps you take to write the fraction.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Write 0.475¯as a fraction. Describe the steps you take to write the fraction.

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

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Write $0 . \bar{475}$ as a fraction. Describe the steps you take to write the fraction.