Question

Use long division to convert 3 4/5%0D%0A3%0D%0A4%0D%0A5%0D%0A to a decimal.(1 point)

Answer 1

To convert \( 3 \frac{4}{5} \% \) to a decimal, we can first convert it into an improper fraction and then divide.

1. **Convert \( 3 \frac{4}{5} \) to an improper fraction:**
\[
3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}
\]

2. **Convert the percentage to a decimal:**
To convert a percentage to a decimal, divide by 100.
\[
\frac{19}{5} \div 100 = \frac{19}{5} \times \frac{1}{100} = \frac{19}{500}
\]

3. **Perform long division to find the decimal equivalent of \( \frac{19}{500} \):**
- Divide 19 by 500.
- Since 19 is less than 500, the integer part of the quotient is 0. Start with 0.
- Write it as \( 0.03 \) (adding decimal places).
- Multiply \( 19 \) by \( 2 \) (which is \( 500 \times 0.02 \)) to reach \( 0.038 \).
- Now, we calculate \( 19.00 \div 500 \):
- 500 goes into 1900 (19.00) three times (3).
- 500 × 3 = 1500.
- Subtract 1500 from 1900, leaving 400.
- Bring down a 0 (to make it 4000).
- 500 goes into 4000 eight times (8).
- 500 × 8 = 4000.
- Subtract 4000 from 4000, leaving 0.

The decimal representation is:
\[
0.038
\]

Thus, \( 3 \frac{4}{5} \% = 0.038 \) in decimal form.