B. Number · Number Sense: Numbers to 100 000, Fractions, Decimals and Percents

Percents: Fractions, Decimals and Percents

B1.7 A1About 40 minutes

Learning goals

I can explain that percent means "out of 100".
I can show a whole-number percent on a hundred grid.
I can write a percent as a fraction and a decimal, and back again.
I can use benchmark percents like 25%, 50%, 75% and 100%.

Words to know

percent (%)
Out of 100. 45% means 45 out of 100, or 45/100.

100%
The whole thing, or all of it.

0%
None of it.

benchmark percents
Friendly percents to know: 10% = 1/10, 25% = 1/4, 50% = 1/2, 75% = 3/4, 100% = 1 whole.

Let's start with a battery

Your tablet's battery icon says 75%. What does that mean?

Percent means "out of 100". If the full battery were split into 100 equal parts, 75 of those parts are still full. 75 out of 100 is 75/100, which is the same as 3/4. Your battery is three quarters full!

Percents, fractions and decimals are partners

A hundred grid shows all three at once. Each small square is 1/100 = 0.01 = 1%.

45 squares shaded = 45/100 = 0.45 = 45%.

A hundred grid with 4 full columns and 5 more squares shaded: 45 squares out of 100.

Percent	Fraction	Decimal
100%	100/100 = 1	1.00
75%	75/100 = 3/4	0.75
50%	50/100 = 1/2	0.5
25%	25/100 = 1/4	0.25
20%	20/100 = 1/5	0.2
10%	10/100 = 1/10	0.1
1%	1/100	0.01
0%	0/100 = 0	0

Benchmark percents and their fraction and decimal partners.

How to change between them

Percent → fraction: write it over 100. 37% = 37/100.
Percent → decimal: 37 hundredths = 0.37.
Fraction → percent: make an equivalent fraction with denominator 100. 3/5 = 60/100 = 60%.
Decimal → percent: read it as hundredths. 0.8 = 0.80 = 80 hundredths = 80%.

🐶🐶🐶🐶🐱🐱🐱🐱🐱🐱

10 pets: 4 dogs and 6 cats.

Worked example

Example 1: Percent to fraction and decimal

Write 37% as a fraction and a decimal.

Percent means out of 100: 37% = 37/100.
37 hundredths as a decimal: 0.37.

37% = 37/100 = 0.37

Worked example

Example 2: Fraction to percent

Write 1/4 as a percent.

Make hundredths: 4 × 25 = 100, so 1/4 = 25/100.
25 out of 100 = 25%.

1/4 = 25%

Worked example

Example 3: Part of a group

Look at the 10 pets. What percent of the pets are dogs? What percent are cats?

4 of the 10 pets are dogs: 4/10.
Make hundredths: 4/10 = 40/100 = 40%.
Cats: 6/10 = 60/100 = 60%.
Check: 40% + 60% = 100%, which is all the pets.

40% dogs and 60% cats.

Worked example

Example 4: Decimal to percent

Write 0.8 as a percent.

0.8 = 0.80 = 80 hundredths.
80 out of 100 = 80%.

0.8 = 80% (not 8%!)

Percents in everyday life

"There is a 60% chance of snow tomorrow." (More likely to snow than not.)
"This juice is 100% juice." (All juice.)
"25% off all winter boots!" (You save 1/4 of the price.)
"I got 90% on my spelling test." (9 out of 10 parts right.)

Make sense of percents

When you see a percent, ask yourself, "Is this more or less than half (50%)? Close to all (100%) or close to none (0%)?" Thinking about benchmarks helps you check that your answer makes sense. If something feels confusing, take a breath and go back to the hundred grid.

Just for fun

What percent of a pizza is left after a hungry family finishes it?

0%, and about 100% of the crumbs are on the table!

Hands-on activity

Percent hunt and hundred grid art

You need: paper, a pencil, a ruler and pencil crayons or markers.

Part 1: Percent hunt. With a grown-up, look for percents around your home: a phone or tablet battery, food labels, clothing tags (like "100% cotton"), store flyers or a weather app. Write down 4 percents you find. For each one, write it as a fraction out of 100 and say if it's more or less than half.

Part 2: Hundred grid art. Draw a 10 by 10 square grid (use a ruler, 1 cm squares work well). Colour a picture or design using 3 colours, and leave some squares blank. Count the squares of each colour and write each one as a fraction, decimal and percent. Check: all your percents (including the blank squares) should add up to 100%.

Your turn

Write 29% as a fraction.

Write 0.53 as a percent.

Write 1/2 as a percent.

Write 3/10 as a percent.

You ate 100% of your pizza. How much did you eat?

9 out of 10 students wore a toque to school. What percent is that?

Write 75% as a fraction with the smallest numbers you can.

More practice: warm-up

Write 50% as a decimal.

Write 10% as a fraction.

What does 0% mean?

46 squares out of 100 are shaded. What percent is that?

Which is more: 30% or 3%?

More practice: on your own

Write 2/5 as a percent.

Write 0.07 as a percent.

25 squares of a hundred grid are shaded. What percent is not shaded?

13 of 20 students like skating best. What percent is that?

The weather app says 70% chance of snow. Is it more likely to snow or not to snow?

Challenge

Order from least to greatest: 0.4, 35%, 1/2, 3/10

There are 25 students in a class. 12 walk to school. What percent walk?

Leah got 18 out of 20 on a quiz. Max got 85%. Who did better?

Check your understanding

Quiz

63% is equal to...

1/4 is equal to...

Percent means...

7 out of 10 is what percent?

100% of something means...

Which is greatest?

For parents and teachers

Big idea: B1.7 includes relating fractions and decimals to whole-number percents (like 45%, not 45.5%). Percents were not part of Grade 4, so this is your child's first formal work with them. The hundred grid is the key tool, because one square is 1/100 = 0.01 = 1%.

Common difficulties:

0.8 = 8%. Write 0.8 as 0.80 first: 80 hundredths = 80%.
Thinking a percent is a count ("40% of the pets" means 40 pets). Percent is always out of 100 parts of the whole.
Fraction to percent with denominators other than 100. Make an equivalent fraction out of 100 first (3/5 = 60/100).

How to help: Point out percents in daily life: battery levels, weather forecasts, sales and labels. Ask "Is that more or less than half?" Strand A is woven in: encourage your child to pause and use a hundred grid when they feel stuck.