62.5% as a decimal and as a fraction. PLEASE SHOW WORK.
The Correct Answer and Explanation is:
To convert 62.5% into a decimal and a fraction, let’s follow these steps:
Step 1: Convert the percentage to a decimal
To convert a percentage into a decimal, you divide by 100. This means:62.5%=62.510062.5\% = \frac{62.5}{100}62.5%=10062.5
Now, perform the division:62.5÷100=0.62562.5 \div 100 = 0.62562.5÷100=0.625
So, 62.5% as a decimal is 0.625.
Step 2: Convert the decimal to a fraction
Now, let’s convert the decimal 0.625 into a fraction. Since 0.625 has three decimal places, we can write it as:0.625=62510000.625 = \frac{625}{1000}0.625=1000625
Next, simplify this fraction. Both 625 and 1000 can be divided by 125 (the greatest common divisor of 625 and 1000):625÷1251000÷125=58\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}1000÷125625÷125=85
Thus, 0.625 as a fraction is 58\frac{5}{8}85.
Final Answer
- 62.5% as a decimal is 0.625.
- 62.5% as a fraction is 58\frac{5}{8}85.
Explanation
- The decimal conversion is straightforward: just divide by 100.
- The fraction conversion involves recognizing that decimals can be expressed as fractions over powers of 10, then simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor.
The key takeaway is that percentages can easily be converted into decimals and fractions, and the fractions can usually be simplified further for clarity.
