Understanding Percentages
Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal
What a learner can do afterwards
- Write 35% as 35/100 and as 0.35
- Shade 40% of a 10×10 grid and write the fraction 40/100
- Explain that 100% means the whole, 50% means half
1 · Read
The symbol % is called percent. Percent means 'out of 100.' When you see 35%, it means 35 out of every 100 equal parts. You already know how to write hundredths as decimals, so percent gives you a new way to write the same amount.
Look at 35%. Since percent means out of 100, you can write it as the fraction 35/100. A fraction with 100 on the bottom is also a decimal with two digits after the point, so 35/100 is the same as 0.35.
100% means the whole thing, all 100 parts. 50% means half, since 50 is half of 100. Whenever you see percent, ask yourself: how many parts out of 100?
Percent means out of 100: write it as a fraction over 100, then as a decimal by counting two places.
More to read
Converting percents and fractions review
Percent means out of one hundred. That is the big idea behind the % sign.
Writing a percent as a fraction: Say the percent in words, then write it as a fraction. For example, 15% means 15 out of one hundred, so 15% = 15/100.
Writing a percent as a decimal: A percent is already a fraction out of 100, so divide by 100. 15% = 15/100 = 0.15. Notice the digits slide two places, because 100 has two zeros.
Writing a decimal as a percent: Go the other way. 0.15 means 15 hundredths, which is 15 out of 100, so 0.15 = 15%.
Try it yourself: Take a 10 by 10 grid. Shade 15 squares. The shaded part is 15/100, which is 15%. Shade all 100 squares and you have 100%, the whole grid. Shade half, 50 squares, and you have 50%, which is one half.
Key Concepts: Understand Percent
Here are the three moves that turn percents, fractions, and decimals into each other.
Percent to fraction: Step 1. Write the percent as a fraction with 100 on the bottom. So 25% becomes 25/100. Step 2. Simplify if you can. 25/100 simplifies to 1/4.
Percent to decimal: Step 1. Write the percent as a fraction with 100 on the bottom. 25% = 25/100. Step 2. Divide the top by 100. 25 divided by 100 is 0.25.
Decimal to percent: Step 1. Write the decimal as a fraction out of 10, 100, or 1000. 0.25 is 25/100. Step 2. Rewrite it as a percent. 25 out of one hundred is 25%.
Remember: 100% is the whole thing, 50% is half, and 25% is one quarter.
Writing decimals as fractions review
A decimal tells you about place value, and that makes it easy to turn into a fraction.
Look at the last digit of the decimal to find its place value. That place value becomes the bottom of the fraction.
Example: 0.07 The 7 is in the hundredths place, so write 7 over 100. 0.07 = 7/100.
Example: 2.1 The 2 is a whole number, so keep it. The 1 is in the tenths place, so 2.1 = 2 and 1/10.
Why this helps with percents: A percent is a number out of one hundred. So a decimal like 0.07, which is 7 hundredths, matches 7% perfectly.
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