Question

Use long division to convert 3 and 3/8 to a decimal

Answer 1

To convert the mixed number \(3\frac{3}{8}\) to a decimal using long division, we will first convert the mixed number into an improper fraction:

\[
3\frac{3}{8} = 3 + \frac{3}{8} = \frac{24}{8} + \frac{3}{8} = \frac{27}{8}
\]

Now, we will divide \(27\) by \(8\) using long division.

1. Set up the division: \(27\) is the dividend, and \(8\) is the divisor.
2. Determine how many times \(8\) goes into \(27\).

- \(8\) goes into \(27\) (3 times):
\[
8 \times 3 = 24
\]
- Write \(3\) above the division line.

3. Subtract \(24\) from \(27\):
\[
27 - 24 = 3
\]

4. Now bring down a zero (since we're looking for a decimal) to make it \(30\).
5. Determine how many times \(8\) goes into \(30\).

- \(8\) goes into \(30\) (3 times):
\[
8 \times 3 = 24
\]
- Write \(3\) after the decimal point above the division line.

6. Subtract \(24\) from \(30\):
\[
30 - 24 = 6
\]

7. Bring down another zero to make it \(60\).
8. Determine how many times \(8\) goes into \(60\).

- \(8\) goes into \(60\) (7 times):
\[
8 \times 7 = 56
\]
- Write \(7\) next to the \(3\).

9. Subtract \(56\) from \(60\):
\[
60 - 56 = 4
\]

10. Bring down another zero to make it \(40\).
11. Determine how many times \(8\) goes into \(40\).

- \(8\) goes into \(40\) (5 times):
\[
8 \times 5 = 40
\]
- Write \(5\) next to the \(37\).

12. Subtract \(40\) from \(40\):
\[
40 - 40 = 0
\]

This means we’ve reached a remainder of \(0\). Therefore, the decimal representation of \(3\frac{3}{8}\) is:

\[
3.375
\]

So, \(3\frac{3}{8} = 3.375\).