B. Number · Number Sense: Big Numbers, Square Roots and Rational Numbers

Converting Between Fractions, Decimals and Percents

B1.7 A1About 45 minutes

Learning goals

I can change a decimal to a percent and a percent to a decimal.
I can change a fraction to a percent and a percent to a fraction in simplest form.
I can work with percents greater than 100% and less than 1%.
I can compare numbers written as fractions, decimals and percents.

Words to know

percent (%)
Out of 100. 35% means 35 out of 100, or 35/100.

equivalent
Having the same value. 1/2, 0.5 and 50% are equivalent.

greater than 100%
More than one whole. 125% = 1.25 = 1 1/4.

less than 1%
Less than one hundredth. 0.5% = 0.005 = 1/200.

Remember from Grade 6

In Grade 6 you learned that percent means out of 100. You wrote ratios like 11 out of 20 as 55%, and found percents like 10% and 25% of a number. Now you will move easily between all three forms, fractions, decimals and percents, including percents over 100% and under 1%.

One number, three outfits

A phone battery shows 35%. That means 35 out of 100 parts are left.

As a fraction: 35/100 = 7/20
As a decimal: 0.35
As a percent: 35%

They are three ways to write the same amount, like one person wearing three different outfits.

Left: 35 of 100 squares shaded is 35%. Right: one full hundred grid plus 25 more squares is 125%, which is more than one whole.

The conversion rules

Decimal → percent: multiply by 100. The decimal point moves 2 places right. 0.35 → 35%; 1.25 → 125%; 0.005 → 0.5%.
Percent → decimal: divide by 100. The decimal point moves 2 places left. 8% → 0.08; 150% → 1.5; 0.3% → 0.003.
Percent → fraction: write it over 100, then simplify. 24% = 24/100 = 6/25.
Fraction → percent: change it to a decimal first (or to an equivalent fraction out of 100), then to a percent. 3/8 = 0.375 = 37.5%.

Follow the arrows to change forms. Decimal ↔ percent is just moving the decimal point 2 places. Example in the middle: 3/8 = 0.375 = 37.5%.

Fraction	Decimal	Percent
1/2	0.5	50%
3/8	0.375	37.5%
5/4 = 1 1/4	1.25	125%
2	2.0	200%
1/200	0.005	0.5%
1/3	0.333…	33.3…% (about 33.3%)

Each row shows the same amount in three forms.

Worked example

Example 1: Decimal → percent → fraction

On a quiz, Jaya scored 0.62 of the marks. Write this as a percent and as a fraction in simplest form.

Decimal → percent: 0.62 × 100 = 62%.
Percent → fraction: 62/100. Divide both by 2: 31/50.

0.62 = 62% = 31/50

Worked example

Example 2: Fraction → percent

Write 7/8 as a percent.

7/8 = 7 ÷ 8 = 0.875.
0.875 × 100 = 87.5.

7/8 = 87.5%

Worked example

Example 3: More than 100%

A bean plant grew to 1.4 times its height from last week. Write 1.4 as a percent and as a mixed number.

1.4 × 100 = 140%. That's more than 100% because it's more than one whole.
1.4 = 1 4/10 = 1 2/5.

1.4 = 140% = 1 2/5. The plant is now 140% of its old height.

Worked example

Example 4: Less than 1%

A savings account pays 0.3% interest per month. Write 0.3% as a decimal and as a fraction.

Percent → decimal: 0.3 ÷ 100 = 0.003 (move the decimal point 2 places left).
0.003 = 3 thousandths = 3/1000.

0.3% = 0.003 = 3/1000. Less than 1% means less than 1/100.

Check with benchmarks

50% = 1/2 = 0.5 and 100% = 1. So a fraction less than 1/2 must be less than 50%, and a decimal greater than 1 must be more than 100%. If your answer breaks these rules, check where you put the decimal point. Common mix-up: 0.06 is 6%, not 60%.

Hands-on activity

Percent hunt

You need: grocery flyers, food packages with a Nutrition Facts table, a phone or tablet showing its battery level, paper and a pencil.

Make a table with four columns: Where I found it, Percent, Decimal, Fraction (simplest form).
Find at least 6 percents: sale signs ("25% off"), the "% Daily Value" on Nutrition Facts tables, battery levels, and anything else you spot.
Fill in the decimal and the fraction for each one.
Look for a percent over 100% or under 1%. (Hint: % Daily Value can sometimes be over 100%, and some Nutrition Facts tables list 0% or 1%.) If you can't find one, make one up and explain what it would mean.
Put your percents in order from least to greatest.

What to look for: correct decimal point moves (25% = 0.25 = 1/4; 8% = 0.08 = 2/25).

Just for fun

A coach yells, "Give me 110%!" But 100% is all of something, so 110% is more than everything you've got. Nice try, coach!

Your turn

Write 0.45 as a percent.

Write 8% as a decimal.

Write 3/5 as a percent.

Write 150% as a decimal and as a mixed number.

Write 0.5% as a decimal.

Write 24% as a fraction in simplest form.

Write 1/8 as a percent.

More practice: warm-up

Write 50% as a fraction.

Write 0.25 as a percent.

Write 1 as a percent.

Write 10% as a decimal.

Write 3/4 as a percent.

More practice: on your own

Write 2.25 as a percent.

Write 0.06 as a percent. Explain why it is not 60%.

Write 5/8 as a percent.

Write 12.5% as a decimal and as a fraction in simplest form.

Write 0.2% as a decimal and as a fraction in simplest form.

Challenge

Order from least to greatest: 0.7, 3/4, 68%, 71.5%

A sunflower was 80 cm tall in June and 200 cm tall in August. Write the August height as a percent of the June height.

Write 1/3 and 2/3 as percents. Why can't you write them exactly with a decimal percent that ends?

Check your understanding

Quiz

What is 0.07 as a percent?

What is 135% as a decimal?

What is 2/5 as a percent?

What is 0.4% as a decimal?

What is 85% as a fraction in simplest form?

Which is the greatest?

What is 1.2 as a percent?

For parents and teachers

Big idea: This lesson completes B1.7: convert between fractions, decimal numbers, and percents, in various contexts. It includes percents greater than 100% and less than 1%. Using percents to increase or decrease amounts (B2.3) and solving percent problems (B2.1) are in the Operations unit.

Common difficulties:

Moving the decimal point the wrong way or the wrong number of places (0.06 → 60%, 8% → 0.8).
Thinking a percent can't be over 100%. Growth and comparisons often give percents over 100%.
Forgetting to simplify the fraction (24% = 24/100 → 6/25).

How to help: Go on a percent hunt with flyers and Nutrition Facts tables. Ask "Is that more or less than half? More or less than one whole?" to build estimation. This lesson builds A1 skills: making connections between representations and checking answers for reasonableness.