Use long division to convert 13/20 to a decimal.

Answer 1

To convert the fraction 13/20 to a decimal using long division, follow these steps:

1. Divide 20 by 13. Write the quotient (1) above the division bar.

```
1
──────
13│20
13
```

2. Multiply the quotient (1) by the divisor (13) and subtract the result from the dividend (20).

```
1
──────
13│20
13
──
7
```

3. Bring down the next digit of the dividend (0).

```
1
──────
13│20
13
──
7
+0
```

4. Divide the new dividend (70) by the divisor (13). Write the quotient (5) above the division bar.

```
1 5
──────
13│20
13
──
7
+0
65
```

5. Multiply the quotient (5) by the divisor (13) and subtract the result from the new dividend (70).

```
1 5
──────
13│20
13
──
7
+0
65
──
5
```

6. Bring down the next digit of the dividend (0).

```
1 5
──────
13│20
13
──
7
+0
65
──
5
+0
```

7. Divide the new dividend (50) by the divisor (13). Write the quotient (3) above the division bar.

```
1 5 3
────────
13│20
13
──
7
+0
65
──
5
+0
52
```

8. Multiply the quotient (3) by the divisor (13) and subtract the result from the new dividend (50).

```
1 5 3
────────
13│20
13
──
7
+0
65
──
5
+0
52
──
-2
```

9. Since the remainder is negative, we can add a decimal point and a zero to the dividend and continue the division.

```
1 5 3
────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
```

10. Divide the new dividend (−20) by the divisor (13). Write the quotient (−1) above the division bar.

```
1 5 3 −1
────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
```

11. Multiply the quotient (−1) by the divisor (13) and subtract the result from the new dividend (−20).

```
1 5 3 −1
────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
```

12. Bring down the next digit of the dividend (0).

```
1 5 3 −1
────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
+0
```

13. Divide the new dividend (−70) by the divisor (13). Write the quotient (−5) above the division bar.

```
1 5 3 −1 −5
──────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
+0
-65
```

14. Multiply the quotient (−5) by the divisor (13) and subtract the result from the new dividend (−70).

```
1 5 3 −1 −5
──────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
+0
-65
────
-50
```

15. Bring down the next digit of the dividend (0).

```
1 5 3 −1 −5
────────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
+0
-65
────
-50
+ 0
```

16. Divide the new dividend (−500) by the divisor (13). Write the quotient (−38) above the division bar.

```
1 5 3 −1 −5 −38
────────────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
+0
-65
────
-50
+ 0
-39
```

17. Multiply the quotient (−38) by the divisor (13) and subtract the result from the new dividend (−500).

```
1 5 3 −1 −5 −38
────────────────────
13│20.0
13
──
7
+0
65
──
5
+0
52
──
-2.0
-1
13
+0
-65
────
-50
+ 0
-39
-39
```

18. Since the remainder (-390) is a multiple of the divisor (13), the long division is complete.

The fraction 13/20 as a decimal is approximately 0.65.