Question
Write \( 28 \% \) as a decimal and as a simplified fraction. 0.28 and \( \frac{7}{25} \) 2,800 and \( \frac{2800}{1} \) 2.8 and \( \frac{28}{100} \) 0.28 and \( \frac{28}{100} \)
Ask by Guzman Ryan. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 28\% \) is \( 0.28 \) as a decimal and \( \frac{7}{25} \) as a simplified fraction.
Solution
To convert \( 28\% \) to a decimal and a simplified fraction, we can follow these steps:
1. **Convert to Decimal:**
- To convert a percentage to a decimal, divide by \( 100 \):
\[
28\% = \frac{28}{100} = 0.28
\]
2. **Convert to Fraction:**
- The fraction representation of \( 28\% \) is \( \frac{28}{100} \).
- Now, we simplify \( \frac{28}{100} \):
- The greatest common divisor (GCD) of \( 28 \) and \( 100 \) is \( 4 \).
- Divide both the numerator and the denominator by \( 4 \):
\[
\frac{28 \div 4}{100 \div 4} = \frac{7}{25}
\]
Thus, \( 28\% \) can be expressed as:
- Decimal: \( 0.28 \)
- Simplified Fraction: \( \frac{7}{25} \)
The correct answer is:
- \( 0.28 \) and \( \frac{7}{25} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To convert \( 28\% \) to a decimal, you simply divide by 100, which gives you \( 0.28 \). To express it as a fraction, you start with \( \frac{28}{100} \) and simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 4. This results in \( \frac{7}{25} \). For a fun context, did you know that percentages date back to ancient Rome? They used a similar concept for tax collection. Today, understanding percentages can empower you to make informed decisions about things like budgeting or shopping sales, so getting them down to a science helps in everyday life!
