Question

Use long division to convert 3 3/8 to a decimal.(1 point)
Responses

3.375
3.375

0.375
0.375

33.75
33.75

2.66

Answer 1

To convert \( 3 \frac{3}{8} \) to a decimal using long division, follow these steps:

1. First, convert \( 3 \frac{3}{8} \) into an improper fraction. To do this, multiply the whole number (3) by the denominator (8) and then add the numerator (3):

\[
3 \times 8 + 3 = 24 + 3 = 27
\]

So, \( 3 \frac{3}{8} = \frac{27}{8} \).

2. Next, divide 27 by 8 using long division:

- \( 8 \) goes into \( 27 \) three times (since \( 8 \times 3 = 24 \)).
- Write down \( 3 \) as the whole number part, and subtract \( 24 \) from \( 27 \):

\[
27 - 24 = 3
\]

- Now, bring down a zero to make it \( 30 \).
- \( 8 \) goes into \( 30 \) three times (since \( 8 \times 3 = 24 \)).
- Write down \( 3 \) after the decimal: the decimal part starts here.
- Subtract \( 24 \) from \( 30 \) again:

\[
30 - 24 = 6
\]

- Bring down another zero to make it \( 60 \).
- \( 8 \) goes into \( 60 \) seven times (since \( 8 \times 7 = 56 \)).
- Write down \( 7 \) after the decimal point.
- Subtract \( 56 \) from \( 60 \):

\[
60 - 56 = 4
\]

- Bring down another zero to make it \( 40 \).
- \( 8 \) goes into \( 40 \) five times (since \( 8 \times 5 = 40 \)).
- Write down \( 5 \) after the decimal point.
- Subtract \( 40 \) from \( 40 \):

\[
40 - 40 = 0
\]

3. Therefore, the decimal representation of \( \frac{27}{8} \) is:

\[
3.375
\]

Final Answer: **3.375**