Enter the number in two equivalent forms. 62.5 5% written as a decimal is 62.5% written as a fraction in simplest form is _
The Correct Answer and Explanation is:
To express 62.5% in two equivalent forms (as a decimal and a fraction), let’s break it down step by step.
1. Converting 62.5% to a decimal:
To convert a percentage to a decimal, divide the percentage by 100. This is because the word “percent” means “per hundred,” so you essentially shift the decimal point two places to the left.
So for 62.5%, you divide 62.5 by 100:62.5%=62.5100=0.62562.5\% = \frac{62.5}{100} = 0.62562.5%=10062.5=0.625
Thus, 62.5% as a decimal is 0.625.
2. Converting 62.5% to a fraction in simplest form:
To convert 62.5% to a fraction, first express 62.5% as a fraction:62.5%=62.510062.5\% = \frac{62.5}{100}62.5%=10062.5
Next, eliminate the decimal by multiplying both the numerator and denominator by 10:62.5100=6251000\frac{62.5}{100} = \frac{625}{1000}10062.5=1000625
Now, simplify this fraction. To do so, find the greatest common divisor (GCD) of 625 and 1000, which is 125. Divide both the numerator and the denominator by 125:625÷1251000÷125=58\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}1000÷125625÷125=85
Thus, 62.5% as a fraction in simplest form is 58\frac{5}{8}85.
Summary:
- 62.5% as a decimal is 0.625.
- 62.5% as a fraction in simplest form is 58\frac{5}{8}85.
This method of converting percentages involves shifting the decimal for decimals and simplifying fractions through common divisors. Both forms represent the same value but in different mathematical expressions.
