Understanding Percents

A percent is a special way to show a part of a whole. You'll explore what "percent" really means, see how percents connect to fractions and decimals, learn how to switch between all three, and then practice with three activities.

What Is a Percent?

The word percent comes from two Latin words: per (for each) and centum (one hundred). So percent means "per hundred", or "out of 100."

A hundred grid is a great way to see this. The whole grid is one whole, and it has 100 equal squares. Every square is 1% of the grid. Drag the slider, tap a square, or pick a percent to shade part of the grid.

The Hundred Grid

100 squares = the whole = 100%

You can also tap any square to shade up to it.

Remember: 100% is the whole thing, 50% is half of it, and 0% is none of it. A percent is just a fraction whose bottom number is always 100.

Percents, Fractions & Decimals Are Connected

Percents, fractions, and decimals are three ways to write the same amount. Here is one-fourth of a whole shown all three ways:

As a fraction

1 part out of 4 equal parts

As a decimal

0.25

25 hundredths

As a percent

25% — 25 out of 100

Some amounts show up all the time. Learn these benchmarks and you can do many conversions in your head:

Converting Between Them

Fraction → percent (way 1: make the bottom 100)

Multiply the top and bottom by the same number so the bottom becomes 100.

= = = 25%

Fraction → percent (way 2: divide, then × 100)

When the bottom won't easily become 100, divide the top by the bottom to get a decimal. Then change the decimal to a percent.

means 3 ÷ 5 = 0.6

0.6 × 100 = 60%

Decimal → percent

Move the decimal point two places to the right. That is the same as multiplying by 100.

0.25 → 25%|0.6 → 60%|0.05 → 5%

Percent → decimal

Move the decimal point two places to the left. Use a zero as a placeholder if you need one.

25% → 0.25|60% → 0.60|8% → 0.08

Percent → fraction

Write the percent over 100, then simplify by dividing the top and bottom by the same number.

60% = = (divide both by 20)

Watch out for zeros! 0.5 is 50%, but 0.05 is only 5%. Always check: does your answer make sense? Half of a whole is 50%, and 5% is a tiny piece.

Why Percents Matter

Percents let us compare parts of different wholes, because every percent is out of the same number: 100.

Who did better?

Ana got 9 out of 10 on her quiz. Ben got 40 out of 50 on his. The quizzes have different totals, so it's hard to tell. Change each score to a percent:

Ana: = = 90%

90%

Ben: = = 80%

80%

Ana did better, 90% to 80%.

In real life: a sale

A pizza place says "50% off." Since 50% is , you pay half. If a pizza costs $20, you save $10 and pay $10.

In real life: a test score

You got 18 out of 20 questions right.

= = 90%

Did you know? Percents can go past 100%. If a plant grows to 200% of its first height, it is twice as tall. And a percent can be less than 1%, like 0.5%, which is half of one hundredth. Percents show up in sales, grades, sports stats, and weather forecasts.

Let's Practice

Three activities: read percents from a grid, shade a grid to match a percent, and match the different ways to write the same amount.

Read the Grid

Look at the shaded part of the hundred grid, then answer the question.

Question 1 of 10Score: 0

Shade the Grid

Tap or drag across the grid to shade the amount you're asked for. Use the buttons to fine-tune.

Round 1 of 4Score: 0

Match the Forms

Fractions, decimals, and percents are three names for the same amount. Pick the one that matches.

Question 1 of 10Score: 0

What's next? Once you're comfortable with what percents are and how they connect to fractions and decimals, you're ready to learn how to find a percent of a number. That's where percents really come to life in problem solving!