Rename 28 percent as a decimal and fraction in its simplest form.
The Correct Answer and Explanation is :
To convert 28 percent into a decimal and a fraction in its simplest form, let’s follow the steps:
1. Convert 28 percent to a decimal
The percentage sign (%) represents “per hundred,” so to convert a percentage to a decimal, divide it by 100.
[
28\% = \frac{28}{100} = 0.28
]
So, 28 percent as a decimal is 0.28.
2. Convert 28 percent to a fraction
To convert 28 percent into a fraction, remember that percent means “per hundred,” so we express 28 percent as a fraction with 100 in the denominator:
[
28\% = \frac{28}{100}
]
Next, simplify this fraction. To do so, we find the greatest common divisor (GCD) of 28 and 100. The prime factors of 28 are ( 2^2 \times 7 ), and the prime factors of 100 are ( 2^2 \times 5^2 ). The greatest common divisor of 28 and 100 is 4. Now, divide both the numerator and denominator by 4:
[
\frac{28}{100} = \frac{28 \div 4}{100 \div 4} = \frac{7}{25}
]
So, 28 percent as a fraction in its simplest form is (\frac{7}{25}).
3. Summary
- Decimal: 28 percent as a decimal is 0.28.
- Fraction: 28 percent as a fraction in simplest form is (\frac{7}{25}).
Explanation:
When converting percentages, remember that “percent” means “per hundred,” so you can convert a percentage by dividing the number by 100. In the case of 28 percent, this gives the decimal 0.28. To convert it into a fraction, you can write it as 28/100, and then simplify it by finding the greatest common divisor (GCD) of 28 and 100. By dividing both the numerator and denominator by 4, you get the fraction (\frac{7}{25}).