To find the decimal expansions of 10/3, 7/8, and 1/7, we can perform long division as follows:
1. 10/3:
``` 3 | 10.000 9 ----- 1.000 9 ----- 100. ```
The remainder is 1, which we bring down to get 10. We add a decimal point and a zero, and then continue the long division process by bringing down another zero and repeating the division:
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To find the decimal expansions of 10/3, 7/8, and 1/7, we can perform long division as follows:1. 10/3:
```
3 | 10.000
9
-----
1.000
9
-----
100.
```
The remainder is 1, which we bring down to get 10. We add a decimal point and a zero, and then continue the long division process by bringing down another zero and repeating the division:
```
3 | 10.000
9
-----
1.000
9
-----
100.
99
---
100
99
--
10.
```
We can see that the decimal expansion of 10/3 is 3.333... (repeating).
2. 7/8:
```
8 | 7.000
0
------
7.000
```
We can see that the decimal expansion of 7/8 is 0.875.
3. 1/7:
```
7 | 1.000
0
------
1.000
-0.7
-----
0.300
-0.28
-----
0.022
-0.21
-----
0.013
-0.07
-----
0.060
-0.56
-----
0.040
-0.35
-----
0.090
-0.84
-----
0.066
-0.63
-----
0.033
```
We can see that the decimal expansion of 1/7 is 0.142857142857... (repeating).
Given :
[tex]= \frac{10}{3} , \frac{7}{8} \: and \: \frac{1}{7} \\ [/tex]
To Find :
[tex]Decimal \: Expansions [/tex]
Solution Required :
[tex] \frac{10}{3} = 3.33 \\ \\ \frac{7}{8} = 0.875 \\ \\ \frac{1}{7} = 0.142[/tex]