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 $0.2\bar{6}$.