Question

Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 point).

Answer 1

Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.

Answer 2

Convert 0.8¯¯¯ to a rational number.

Answer 3

To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by what number?

Answer 4

All of the given rational numbers can be expressed as a repeating decimal except for 5/12.

The decimal representation of 5/12 is 0.4166666666666667. It does not repeat.

Answer 5

To express 7/13 as a repeating decimal, we can use long division:

```
0.53846153846...
_______________
13 | 7.0000000000
-6.5
------
5.0
-3.9
----
1.10
- 0.91
-----
0.19
-0.13
-----
0.6
-0.52
-----
0.8
-0.78
-----
0.20
-0.13
-----
0.7
-0.65
-----
0.5
-0.39
-----
0.110
-0.065
------
0.45
-0.39
------
0.60
-0.52
------
0.80
-0.78
------
0.20
```

The repeating decimal of 7/13 is 0.538461538461... with the digits 538461 repeating.

Answer 6

To convert 0.8¯¯¯ to a rational number, we can use the following steps:

Let x = 0.8¯¯¯.

Since there is a repeating decimal, we can multiply both sides of the equation by 10 to shift the decimal point:

10x = 8.¯¯¯¯¯¯¯¯¯¯.

Subtracting the original equation from the new equation, we get:

10x - x = 8.¯¯¯¯¯¯¯¯¯¯ - 0.¯¯¯8.

Simplifying both sides of the equation, we have:

9x = 8.

Dividing both sides by 9, we get:

x = 8/9.

So, 0.8¯¯¯ can be expressed as the rational number 8/9.

Answer 7

To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100.