Percentages

Out of one hundred

Percent means "out of 100". The word comes from Latin per centum: per cent, "for each hundred". The symbol is %.

• 45% means 45 out of 100.
• 100% is the whole.
• 0% is none.

A percent is a ratio that always compares to 100.

Picturing percent

On a hundred grid (10 × 10 squares):

Percent, fraction, decimal

A percent can be written as a fraction over 100 or as a decimal.

Benchmark percents

Learn these benchmark percents; they help with mental maths:

From these you can build others: 5% = half of 10%; 75% = 50% + 25%; 20% = 2 × 10%.

More than 100% and less than 1%

• 150% means one and a half times the whole. If a plant grows to 150% of its height, it is 1.5 times as tall.
• 0.5% means half of one percent: 0.005.

Where we see percents

• Test scores: 18/20 = 90%
• Sales: 30% off
• Battery level: 62%
• Weather: 40% chance of rain
• Taxes: 13% HST in Ontario

Worked examples

Example 1: 37 of 100 squares are shaded. What percent?

37%.

Example 2: What percent is 1/4?

1/4 = 25/100 = 25%.

Example 3: A class has 25 students; 20 are present. What percent are present?

20/25 = 80/100 = 80%.

Common mistakes

• Thinking percents can’t go over 100. They can (e.g. 200% is double).
• Mixing up 0.5 and 0.5%. 0.5 is 50%; 0.5% is 0.005.
• Forgetting what the whole is. "50% of what?" always matters.

Try it yourself

1. Write 63% as a fraction.
2. Write 3/10 as a percent.
3. What is 10% of 250?
4. What is 25% of 48?
5. 18 out of 20 is what percent?

Answers: 1) 63/100 2) 30% 3) 25 4) 12 5) 90%

Quick recap

• Percent means "out of 100"; 100% is the whole.
• Percents, fractions and decimals are three ways to show the same value.
• Use benchmark percents (10%, 25%, 50%) for quick calculations.