# To express: 0. 7 ¯ repeating decimal as a fraction.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 75E

(a)

To determine

Expert Solution

## Answer to Problem 75E

0.7¯=79

### Explanation of Solution

Given information:

0.7¯

Calculation:

The given repeating decimal is 0.7¯

A repeating decimal such as x=0.777777 ……………is a rational number

To convert it to a ration of two integers, we write

100x=77.777710x=7.7777_90x=70

Thus, x=7090=79

The idea is to multiply x by the appropriate powers of 10, and then subtract to eliminate the repeating part.

(b)

To determine

Expert Solution

## Answer to Problem 75E

0.28¯=1645

### Explanation of Solution

Given information:

0.28¯

Calculation:

The given repeating decimal is 0.28¯

A repeating decimal such as x=0.288888 ……………is a rational number

To convert it to a ration of two integers, we write

100x=28.888810x=2.8888_90x=26x=2690=1645

(c)

To determine

Expert Solution

## Answer to Problem 75E

0.57¯=1933

### Explanation of Solution

Given information:

0.57¯

Calculation:

The given repeating decimal is 0.57¯

A repeating decimal such as x=0.575757 ……………is a rational number

To convert it to a ration of two integers, we write

10000x=5757.57100x=57.57_9900x=5700x=5799=1933

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