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

Comparing and Ordering Decimals to Hundredths

B1.5 A1About 35 minutes
Learning goals
  • I can compare decimals by lining up the decimal points.
  • I can explain why a decimal with more digits is not always greater.
  • I can order decimals from least to greatest and greatest to least.
  • I can compare decimals in real life, like jumps, prices and race times.

Words to know

line up
Write numbers one above the other so the decimal points (and places) are in a column.
equivalent decimals
Decimals that name the same amount, like 0.5 and 0.50.

Remember from Grade 4

In Grade 4 you compared decimal tenths, like 2.6 and 2.9. You looked at the whole numbers first, then the tenths. Now we add the hundredths place.

Let's start at track and field day

Ana jumped 2.35 m in the long jump. Ben jumped 2.5 m. Ana says, "I won, because 35 is more than 5!"

Is Ana right? Let's line up the numbers.

Ones.TenthsHundredths
Ana2.35
Ben2.50
Write 2.5 as 2.50 so both numbers have hundredths. Same ones (2). Tenths: 3 < 5.

How to compare decimals

  1. Line up the decimal points.
  2. If needed, add zeros at the end so both numbers have the same number of decimal places. (2.5 = 2.50.)
  3. Compare from the left, just like whole numbers. The first place that is different decides.

2.35 < 2.50, so Ben jumped farther. Ana's mistake: the 5 in 2.5 means 5 tenths, which is the same as 50 hundredths. More digits doesn't mean bigger!

22.12.22.32.42.52.62.72.82.932.352.5
A number line from 2 to 3. Each long tick is a tenth. 2.35 is between 2.3 and 2.4. 2.5 is halfway between 2 and 3.
Worked example

Example 1: Tenths vs hundredths

Compare 0.8 and 0.75.

  1. Line up and write 0.8 as 0.80.
  2. Ones: 0 = 0. Tenths: 8 > 7.

0.8 > 0.75

0.8 = 0.800.7580 hundredths75 hundredths>
0.8 fills 8 full columns (80 small squares). 0.75 fills 7 columns and 5 more squares (75). So 0.8 > 0.75, even though 0.75 has more digits.
Worked example

Example 2: Order a list

Order from least to greatest: 4.09, 4.9, 4.19, 4.91

  1. Write them all with hundredths: 4.09, 4.90, 4.19, 4.91.
  2. All have 4 ones. Tenths: 0, 9, 1, 9. So 4.09 is least, then 4.19.
  3. 4.90 and 4.91 both have 9 tenths. Hundredths: 0 < 1.

4.09, 4.19, 4.9, 4.91

Worked example

Example 3: When less is better

Three swimmers raced 50 m. Their times were 38.42 s, 38.24 s and 39.05 s. Who won?

  1. In a race, the least time is the fastest.
  2. 39.05 has 39 seconds, so it's the slowest.
  3. 38.42 vs 38.24: tenths 4 > 2, so 38.24 is less.

The swimmer with 38.24 s won.

Worked example

Example 4: Find a decimal in between

Name a decimal between 2.3 and 2.4.

  1. Write them as hundredths: 2.30 and 2.40.
  2. Any number from 2.31 to 2.39 is in between.

For example, 2.35.

Be a good sport

At track and field day, cheer for everyone. Comparing results helps you see how you've improved, not just who won. Try to beat your own best jump!

Just for fun

If Ana's rule "more digits means bigger" were true, a 0.99 m jump would beat a 1.5 m jump. The long-jump judges would need a very long meeting!

Hands-on activity

Family long jump

You need: a measuring tape, painter's tape or a sock to mark lines, paper and a pencil, and a clear, soft space (like grass or a carpet) with a grown-up watching. Jump in running shoes or bare feet, not in socks, so you don't slip.

  1. Mark a start line. Each person does a standing long jump (two feet together, jump forward, land on two feet).
  2. Measure from the start line to the back of the closest heel, in centimetres. Write it in metres with two decimal places. For example, 128 cm = 1.28 m.
  3. Everyone jumps 3 times. Record all the jumps.
  4. Circle each person's best jump. Order all the best jumps from greatest to least.
  5. Use > or < to compare your best jump with your first jump. Did you improve?

Your turn

1

Use >, < or =: 0.6 ___ 0.59

2

Use >, < or =: 3.42 ___ 3.24

3

Use >, < or =: 1.7 ___ 1.70

4

Use >, < or =: 0.05 ___ 0.5

5

Order from least to greatest: 0.4, 0.35, 0.48

6

Which price is greatest: $4.09, $4.90, $4.19?

7

Name a decimal between 0.7 and 0.8.

More practice: warm-up

1

Use >, < or =: 0.2 ___ 0.7

2

Use >, < or =: 5.1 ___ 4.9

3

Use >, < or =: 0.30 ___ 0.3

4

Which is less: 0.01 or 0.1?

5

Order from greatest to least: 3.5, 3.05, 3.55

More practice: on your own

1

Order from least to greatest: 1.09, 1.9, 0.99, 1.19

2

Kim says 0.45 > 0.6 because 45 > 6. Is she right?

3

Three long jumps: 2.08 m, 2.8 m, 2.18 m. Which is longest?

4

Two ski racers' times are 52.61 s and 52.16 s. Which time is faster?

5

Name a decimal between 5.6 and 5.7.

Challenge

1

What digits could go in the box? 3.□6 > 3.75

2

Order from least to greatest: 10.1, 1.01, 1.1, 0.11

3

Rainfall this week: Monday 1.25 cm, Tuesday 1.3 cm, Wednesday 1.05 cm, Thursday 1.35 cm. Order the days from most to least rain.

Check your understanding

Quiz

1.

Which is greater?

2.

Which is true?

3.

Which list is in order from least to greatest?

4.

Race times: 12.45 s, 12.54 s, 12.5 s. Which is the fastest?

5.

Which number is between 5.6 and 5.7?

6.

What is a good first step to compare 3.8 and 3.75?

For parents and teachers

Big idea: B1.5 includes comparing and ordering decimals to hundredths in various contexts. The key idea: line up the decimal points and compare place by place from the left.

Common difficulties:

  • "Longer is bigger" (thinking 0.45 > 0.6 or 2.35 > 2.5). Write both with the same number of decimal places, or shade both on a hundred grid.
  • "Shorter is bigger" (some children overcorrect and think 0.3 > 0.35 because tenths are bigger than hundredths). Again, write 0.30 vs 0.35.
  • Context: in races, the least time wins.

How to help: Compare prices in flyers, results in sports, and measurements. During the long-jump activity, make sure the space is clear and soft. Strand A is woven in through good sportsmanship and focusing on personal improvement.