Use long division to convert 4/15 to a decimal.(1 point)

Answer 1

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

1. Set up the long division by dividing 4 by 15. Since 4 is less than 15, we can start the decimal by adding a decimal point and a zero to 4. This makes it 4.0.

2. Now, divide 15 into 40 (since 15 cannot go into 4):

   • 15 goes into 40 2 times (because \( 15 \times 2 = 30 \)).

3. Write down 2 after the decimal point, and then subtract 30 from 40: \[ 40 - 30 = 10 \]

4. Bring down another zero (making it 100):

5. Now, divide 15 into 100:

   • 15 goes into 100 6 times (because \( 15 \times 6 = 90 \)).

6. Write down 6: \[ 100 - 90 = 10 \]

7. Bring down another zero (making it 100 again):

8. Repeat the division:

   • 15 goes into 100 6 times again.

9. Subtract again: \[ 100 - 90 = 10 \]

10. Bring down another zero, and you see we are repeating the process over again.

By repeating these steps, we find that \( \frac{4}{15} = 0.2666...\), where the 6 repeats indefinitely.

Thus, the decimal representation of \( \frac{4}{15} \) is \( 0.2\overline{6} \).