What is 65% as a decimal and fraction in simplest form
The Correct Answer and Explanation is:
Correct answer:
- Decimal: 0.65
- Fraction (simplest form): 13⁄20
Explanation:
To convert 65% into both a decimal and a fraction, we follow a few easy steps. Let’s begin with the decimal.
Step 1: Convert 65% to a Decimal
Percent means “per hundred,” so 65% means 65 out of 100. To change a percent to a decimal, we divide by 100.
So,
65 ÷ 100 = 0.65
This is the decimal form of 65%.
Step 2: Convert 65% to a Fraction
Again, since percent means “per hundred,” we can write 65% as:
65% = 65⁄100
Now we simplify this fraction to its lowest terms. To do this, we find the greatest common factor (GCF) of 65 and 100.
- The factors of 65 are: 1, 5, 13, 65
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor is 5.
Now divide both the numerator and the denominator by 5:
65 ÷ 5 = 13
100 ÷ 5 = 20
So, 65% = 13⁄20 in simplest form.
Summary
- Decimal: 0.65
- Fraction (simplest form): 13⁄20
These conversions are useful in real life, such as in shopping discounts, statistics, and measurements. Being able to switch between percentages, decimals, and fractions helps in comparing quantities and solving problems more easily.
