Question

Use long divisions to convert 4/15 to a decimal

Answer 1

To convert the fraction \( \frac{4}{15} \) to a decimal using long division, follow these steps:

1. **Set up the division**: You're dividing 4 by 15.

\[
4 ÷ 15
\]

2. **Since 4 is less than 15**, you will add a decimal point and zeros to continue the division. Rewrite 4 as 4.000. Now you are calculating \( 40.00 ÷ 15 \).

3. **Perform the long division**:

- **15 goes into 40**: 2 times (because \( 15 \times 2 = 30 \)).
- **Subtract**: \( 40 - 30 = 10 \).
- **Bring down the next 0**: Now you have 100.

4. **Continue dividing**:

- **15 goes into 100**: 6 times (because \( 15 \times 6 = 90 \)).
- **Subtract**: \( 100 - 90 = 10 \).
- **Bring down the next 0**: Now you have 100 again.

5. **Repeat**:

- **15 goes into 100**: 6 times (again).
- **Subtract**: \( 100 - 90 = 10 \).
- **Bring down the next 0**: You will see that it will again yield 100.

6. **It becomes apparent** that the pattern will repeat. Each time you perform the division from \( 100 \), you'll get 6 with a remainder of 10, leading to another 100.

So, the decimal representation of \( \frac{4}{15} \) is:

\[
0.2666...
\]

This can also be noted as \( 0.2\overline{6} \), indicating that the digit 6 repeats indefinitely. Thus:

\[
\frac{4}{15} = 0.26666...
\]