Grade by Grade
B. Number · Number Sense: Numbers to 10 000, Fractions and Decimal Tenths

Comparing and Ordering Decimal Tenths

B1.7 A1About 35 minutes
Learning goals
  • I can compare two decimal tenths using place value.
  • I can use a number line to compare and order decimals.
  • I can order decimals from least to greatest and greatest to least.
  • I can solve problems by comparing decimals in real life.

Words to know

compare
Decide which is greater, which is less, or if they are equal.
order
Put numbers in a line from least to greatest or greatest to least.
decimal tenths
Numbers like 2.6 that have a tenths place.

Let's start with a story

At the Grade 4 long jump, three friends jump:

  • Noor: 2.6 m
  • Leo: 2.9 m
  • Kim: 3.1 m

Who jumped farthest? Kim jumped more than 3 whole metres. Noor and Leo jumped 2 whole metres and some tenths. So Kim jumped the farthest.

How to compare decimals

It works just like whole numbers. Compare from the left.

  1. Compare the whole number parts first. The greater whole number wins.
  2. If the whole numbers are the same, compare the tenths.

2.6 vs 2.9: both have 2 wholes. 6 tenths < 9 tenths, so 2.6 < 2.9.

22.533.5
The long jumps on a number line: 2.6, 2.9 and 3.1. Farther right means greater.
Worked example

Example 1: Same wholes

Compare 4.5 and 4.8.

  1. Wholes: 4 and 4. Same.
  2. Tenths: 5 and 8. 5 tenths < 8 tenths.

4.5 < 4.8

Worked example

Example 2: Different wholes

Compare 0.9 and 1.2.

  1. Wholes: 0 and 1. 0 < 1.
  2. Don't be fooled by the 9! It is only 9 tenths, which is less than 1 whole.

0.9 < 1.2

Worked example

Example 3: Decimal and whole number

Compare 3 and 2.9.

  1. 3 is the same as 3.0.
  2. Wholes: 3 and 2. 3 > 2.

3 > 2.9. 2.9 is 1 tenth less than 3.

Worked example

Example 4: Order a set

Snow fell on 4 days: 1.5 cm, 0.8 cm, 2.0 cm, 1.2 cm. Order the amounts from greatest to least.

  1. Wholes first: 2.0 has 2 wholes. It is the greatest.
  2. 1.5 and 1.2 both have 1 whole. Compare tenths: 5 > 2, so 1.5 > 1.2.
  3. 0.8 has 0 wholes, so it is the least.

2.0 cm, 1.5 cm, 1.2 cm, 0.8 cm

0.810.2
Top bar: 0.8 (8 tenths shaded). The next two bars show 1.2: one whole bar and 2 tenths of another bar. 1.2 is more than 0.8.

Check and fix

If two decimals look tricky, draw them as tenths bars or put them on a number line. If you made a mistake, that's okay: find the step that went wrong and try again. That's how mathematicians learn!

Just for fun

In 0.9 and 1.2, the 9 looks big and tough. But it's only 9 tenths, and the 1 whole in 1.2 wins. Don't let a show-off digit fool you!

Hands-on activity

Paper airplane distances

You need: a sheet of paper (to fold an airplane), a tape measure or metre stick, a pencil and paper. Fly the plane where it can't hit anyone or anything breakable.

  1. Fold a paper airplane.
  2. Stand at a starting line and throw it 5 times. Each time, measure how far it flew to the nearest 10 cm. Write it in metres, like 140 cm = 1.4 m.
  3. Order your 5 distances from least to greatest.
  4. Change one thing about your plane (fold the wing tips, add a paper clip). Throw 5 more times and order those distances.
  5. Compare: Which plane flew the farthest? Use > or <.

Math talk: "How did you decide which distance was the longest?"

Your turn

1

Compare with > or <: 0.4 □ 0.7

2

Compare with > or <: 5.1 □ 4.9

3

Compare with >, < or =: 2.0 □ 2

4

Compare with > or <: 0.9 □ 1

5

Order from least to greatest: 3.4, 3.1, 3.8

6

Order from greatest to least: 6.2, 7.0, 6.9

7

Which is longer: a 1.5 m scarf or a 1.3 m scarf?

More practice: warm-up

1

Which is greater: 0.2 or 0.6?

2

Which is greater: 3.5 or 2.5?

3

Which is less: 8.1 or 8.4?

4

Compare: 1.0 □ 0.1

5

Order from least to greatest: 0.5, 0.1, 0.9

More practice: on your own

1

Order from least to greatest: 2.3, 3.2, 2.9, 0.3

2

Write a decimal between 4.6 and 4.9.

3

Temperatures on three days: 18.5 °C, 21.0 °C, 18.9 °C. Which day was warmest? Which was coolest?

4

Which digits can go in the box? 5.□ > 5.6

5

Is 10.1 greater or less than 9.9? Explain.

Challenge

1

Jo says 4.9 > 5.1 because 9 is bigger than 1. Is she right? Explain.

2

Three ribbons are 1.2 m, 0.9 m and 1 m long. Order them from shortest to longest.

3

Use the digits 3, 7 and 5 once each to make a decimal shaped like □□.□ (two digits, the point, one digit). Make the greatest and the least decimal you can.

Check your understanding

Quiz

1.

Which is true?

2.

Which is the greatest?

3.

Which list is in order from least to greatest?

4.

Which decimal is between 6.4 and 6.7?

5.

A snail crawled 0.6 m and a slug crawled 0.4 m. Which is true?

6.

Compare: 7 □ 6.9

For parents and teachers

Big idea: B1.7 includes comparing and ordering decimal tenths. Children use the same place value thinking as with whole numbers: compare the whole number part first, then the tenths.

Common difficulties:

  • Ignoring the whole number (thinking 0.9 > 1.2 because 9 > 2).
  • Treating the decimal part like a whole number, especially if they see things like 0.10. In Grade 4, decimals have only one digit after the point.
  • Comparing a whole number to a decimal (3 vs 2.9). Write 3 as 3.0.

How to help: Compare real decimals: two thermometer readings, race times, distances on a trail map. Ask "Which is more? How do you know?" Strand A: celebrate fixing mistakes; finding where a mistake happened is a real math skill.