Express the following as a fraction in its lowest terms: 62.5%. Please tell me the solution, please.
The Correct Answer and Explanation is:
To express 62.5% as a fraction in its lowest terms, let’s break down the process step by step.
Step 1: Convert the percentage to a decimal.
First, recall that the percentage symbol (%) means “per 100.” So, we can write 62.5% as:62.5%=62.510062.5\% = \frac{62.5}{100}62.5%=10062.5
Step 2: Remove the decimal point.
To eliminate the decimal, we can multiply both the numerator and the denominator by 10. This moves the decimal one place to the right:62.5100=6251000\frac{62.5}{100} = \frac{625}{1000}10062.5=1000625
Step 3: Simplify the fraction.
Now, we need to simplify the fraction 6251000\frac{625}{1000}1000625 by finding the greatest common divisor (GCD) of 625 and 1000.
- 625 is a multiple of 25, and so is 1000. We can divide both the numerator and the denominator by 125, their GCD:
6251000=625÷1251000÷125=58\frac{625}{1000} = \frac{625 \div 125}{1000 \div 125} = \frac{5}{8}1000625=1000÷125625÷125=85
Step 4: Conclusion.
Therefore, 62.5% as a fraction in its lowest terms is:58\boxed{\frac{5}{8}}85
Explanation:
- Converting a percentage to a fraction involves dividing the percentage by 100.
- Simplifying a fraction requires finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by that number to reduce the fraction to its simplest form.
- In this case, 6251000\frac{625}{1000}1000625 simplifies to 58\frac{5}{8}85, which is the final answer.
By following these steps, we can convert any percentage to its simplest fractional form!
