Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 point).
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.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
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.
Convert 0.8¯¯¯ to a rational number.
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.