# To express: repeating decimal 5. 23 ¯ 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 76E

(a)

To determine

## To express: repeating decimal 5.23¯ as a fraction.

Expert Solution

5.23¯=51899

### Explanation of Solution

Given information:

5.23¯

Calculation:

The given repeating decimal is 5.23¯

A repeating decimal such as x=5.232323 ……………is a rational number

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

1000x=5232.3232310x=52.32323_900x=5180x=5180990=51899

(b)

To determine

Expert Solution

1.37¯=13699

### Explanation of Solution

Given information:

1.37¯

Calculation:

The given repeating decimal is 1.37¯

A repeating decimal such as x=1.37373737 ……………is a rational number

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

1000x=1373.7373710x=13.72737_990x=1360x=1360990=13699

(c)

To determine

Expert Solution

2.135¯=1057495

### Explanation of Solution

Given information:

2.135¯

Calculation:

The given repeating decimal is 2.135¯

A repeating decimal such as x=2.135353535 ……………is a rational number

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

10000x=2135.353510x=_21.3535990x=2114x=2114990=1057495

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