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

Fractions and Decimals to Hundredths

B1.7About 40 minutes

Learning goals

I can write a fraction in tenths or hundredths as a decimal, and a decimal as a fraction.
I can use equivalent fractions to change halves, fourths and fifths into decimals.
I can write mixed numbers as decimals, like 2 3/4 = 2.75.
I can use coins to show how fractions and decimals are related.

Words to know

equivalent
Equal in value. 1/4 and 0.25 are equivalent.

quarter
One fourth (1/4). A quarter coin is 1/4 of a dollar: $0.25.

decimal fraction
A fraction with a denominator of 10 or 100, like 7/10 or 37/100.

Remember from Grade 4

In Grade 4 you learned that fractions in tenths can be written as decimals: 3/10 = 0.3. You also showed that 1/2 = 5/10 = 0.5 and that fifths can become tenths, like 2/5 = 4/10 = 0.4. This year you'll connect fractions and decimals to hundredths.

Let's start with a coin

Why is a quarter called a quarter? Because 4 quarters make $1. So one quarter is 1/4 of a dollar.

A quarter is worth 25 cents, which is $0.25. So 1/4 = 0.25!

Tenths and hundredths change right away

7/10 = 0.7
37/100 = 0.37
7/100 = 0.07 (7 hundredths needs a 0 in the tenths place)

Other fractions: make tenths or hundredths first

Use equivalent fractions to change the denominator to 10 or 100:

1/2 = 50/100 = 0.5 (or 0.50)
1/4 = 25/100 = 0.25
3/4 = 75/100 = 0.75
1/5 = 2/10 = 0.2

Three hundred grids. Half of the first grid is shaded (50 squares), a quarter of the second (25 squares) and three quarters of the third (75 squares).

Fraction	Tenths or hundredths	Decimal
1/2	5/10 or 50/100	0.5
1/4	25/100	0.25
3/4	75/100	0.75
1/5	2/10	0.2
2/5	4/10	0.4
3/5	6/10	0.6
4/5	8/10	0.8

Fractions and decimals that are good to know.

Coin	Fraction of $1	Decimal
quarter (25¢)	1/4	$0.25
dime (10¢)	1/10	$0.10
nickel (5¢)	1/20	$0.05
loonie	1	$1.00

Canadian coins as fractions and decimals of a dollar.

Canadian coins as fractions and decimals of a dollar. The loonie has 11 sides. A dime is smaller than a nickel but worth more: 1/10 of a dollar instead of 1/20.

Worked example

Example 1: Hundredths

Write 7/100 as a decimal.

7 hundredths: there are no tenths, so the tenths place gets a 0.
The 7 goes in the hundredths place.

0.07

Worked example

Example 2: Make hundredths

Write 3/4 as a decimal.

4 × 25 = 100, so multiply the top and bottom by 25.
3 × 25 = 75. So 3/4 = 75/100.

3/4 = 0.75. (Think: 3 quarters = 75 cents.)

Worked example

Example 3: Decimal to fraction

Write 0.8 as a fraction in fifths.

0.8 = 8/10.
Divide the top and bottom by 2: 8/10 = 4/5.

0.8 = 8/10 = 4/5

Worked example

Example 4: Mixed number

Write 1 2/5 as a decimal.

The whole number stays in front of the decimal point: 1.
2/5 = 4/10 = 0.4.

1 2/5 = 1.4

Think in coins

If you remember that 1/4 = 0.25 (a quarter) and 1/2 = 0.5 (two quarters), you can work out 3/4 = 0.75 (three quarters) in your head. Coins are a great memory helper!

Just for fun

Funny but true: Canada's $1 coin is called the loonie because it has a loon on it. When the $2 coin arrived in 1996, people nicknamed it the toonie, a mix of "two" and "loonie"!

Hands-on activity

Coin fractions

You need: some coins (quarters, dimes and nickels) and paper.

Make $1 with quarters. How many? (4.) So one quarter = 1/4 of a dollar = $0.25.
Make $1 with dimes (10) and with nickels (20). Write each coin as a fraction and decimal of a dollar.
Your grown-up says a fraction of a dollar: 1/2, 3/4, 3/10, 1/5. Show it with coins and write it as a decimal. (Check: $0.50, $0.75, $0.30, $0.20.)
Draw a 10 by 10 grid on paper. Shade 1/4 of it. Count the small squares: is it 25?

Your turn

Write 9/10 as a decimal.

Write 63/100 as a decimal.

Write 1/2 as a decimal.

Write 0.25 as a fraction.

Write 4/5 as a decimal.

Write 3 1/4 as a decimal.

Write 0.07 as a fraction.

More practice: warm-up

Write 3/10 as a decimal.

Write 0.5 as a fraction.

Write 1/100 as a decimal.

A dime is what fraction of a dollar?

Write 3/4 as a decimal.

More practice: on your own

Write 2/5 in hundredths, then as a decimal.

Write 0.6 as a fraction in fifths.

Write 2 1/2 as a decimal.

Order from least to greatest: 0.3, 1/4, 1/2

You have 3 quarters. What fraction of a dollar is that? Write it as a decimal too.

Challenge

Write 1/20 as a decimal. (Hint: think of a nickel.)

Which is greater: 1 3/5 or 1.55?

Which is greater: 7/10 or 0.69?

Check your understanding

Quiz

0.4 is equal to...

1/4 is equal to...

3/5 is equal to...

2 3/4 is equal to...

0.09 is equal to...

Which is not equal to 1/2?

For parents and teachers

Big idea: B1.7 asks Grade 5 students to describe relationships and show equivalences among fractions, decimals up to hundredths, and whole-number percents, using tools and drawings. This lesson covers fractions and decimals; the next adds percents.

Common difficulties:

Writing the digits of the fraction as a decimal (1/4 = 0.14, or 3/5 = 0.35). A fraction must first be changed to tenths or hundredths.
Forgetting the 0 placeholder (7/100 = 0.7). Count the places: hundredths need two decimal places.
Not seeing 0.5 and 1/2 as the same number. Shade a hundred grid both ways.

How to help: Coins are the best tool: a quarter is 1/4 of a dollar and $0.25. Ask questions like "What fraction of a dollar is 3 dimes?" (3/10 = $0.30).