Question

Use long division to convert 27/50 to a decimal.

Answer 1

To convert the fraction \( \frac{27}{50} \) to a decimal using long division, we can follow these steps:

1. Set up the long division of 27 by 50. Since 27 is less than 50, we'll add a decimal point and a zero, turning this into 27.0, which allows us to divide it into the tenths place.

```
0.54
__________
50 | 27.00
```

2. Determine how many times 50 can go into 270 (27.0 with added zero). Since 50 goes into 270 five times (because \( 50 \times 5 = 250 \)):

```
0.54
__________
50 | 27.00
-250
------
200
```

3. Subtract 250 from 270, which leaves us with 20. Bring down another 0 to make it 200.

```
0.54
__________
50 | 27.00
-250
------
200
```

4. Now see how many times 50 fits into 200. It fits four times, since \( 50 \times 4 = 200 \):

```
0.54
__________
50 | 27.00
-250
------
200
-200
------
0
```

5. Subtract 200 from 200, which gives you 0.

Since there is no remainder, the division process is complete, and we find that:

\[
\frac{27}{50} = 0.54
\]

Thus, the decimal representation of \( \frac{27}{50} \) is \( 0.54 \).