Question
24. Write \( \frac{4}{11} \) as a a decimal and \( \mathbf{b} \) percent
Ask by Watson Erickson. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{4}{11} \) is approximately 0.\(\overline{36}\) as a decimal and 36.\(\overline{36}\%\) as a percent.
Solution
1. **Convert \( \frac{4}{11} \) to a decimal**
To convert the fraction \( \frac{4}{11} \) into a decimal, perform the division:
\[
4 \div 11 \approx 0.363636\ldots
\]
This is a repeating decimal and it can be written as:
\[
0.\overline{36}
\]
2. **Convert the decimal to a percent**
To change the decimal \( 0.\overline{36} \) to a percent, multiply by \( 100 \):
\[
0.\overline{36} \times 100 \approx 36.\overline{36}\%
\]
Hence, \( \frac{4}{11} \) is approximately \( 36.\overline{36}\% \).
3. **Final Answers:**
\[
\frac{4}{11} \approx 0.\overline{36} \quad \text{(as a decimal)}
\]
\[
\frac{4}{11} \approx 36.\overline{36}\% \quad \text{(as a percent)}
\]
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Simplify this solution The Deep Dive
When you convert \( \frac{4}{11} \) to a decimal, you can accomplish this by dividing 4 by 11, which gives approximately 0.3636. This is a repeating decimal, often written as \( 0.\overline{36} \) to indicate that the digits 36 repeat indefinitely. To express \( \frac{4}{11} \) as a percent, simply multiply the decimal result by 100. So, \( 0.3636 \times 100 = 36.36\% \). Therefore, \( \frac{4}{11} \) is about 36.36% when expressed as a percentage!
