Ordering decimals: what children learn
In this game children put five decimals in order, either smallest first or largest first. Each set is built from the same few digits in different places, with different numbers of decimal places, so the only way to order them is to compare place by place. Move cards with the arrow buttons or tap two cards to swap them.
Supports part of Common Core 5.NBT.A.3.b. This focused game does not cover the entire standard.
Common Core connection: 5.NBT.A.3.b. This is focused practice for part of the standard.
How to play
Put the numbers in order. Use the arrow buttons, or pick one card and then another to swap them. Each game has 5 rounds. After you press Check, the correct order is shown if you got it wrong.
Step by step
- Compare the whole numbers first. 1.08 is bigger than 0.95 because 1 whole is more than 0 wholes.
- Then compare tenths. If the whole numbers match, look at the first digit after the point. 0.5 has 5 tenths and 0.45 has 4 tenths, so 0.5 is bigger.
- Then hundredths, then thousandths. If the tenths match too, compare the next digit: 0.45 and 0.405 both have 4 tenths, but 0.45 has 5 hundredths while 0.405 has 0. So 0.45 is bigger.
- Fill gaps with zeros to help. Writing every number with three decimal places makes comparing easier: 0.500, 0.450, 0.405, 0.054.
Worked examples
Example 1: Order 0.5, 0.45, 0.405, 0.054, 0.54, smallest first.
Working: Write them with 3 dp: 0.500, 0.450, 0.405, 0.054, 0.540. Compare tenths, then hundredths.
Answer: 0.054, 0.405, 0.45, 0.5, 0.54
Example 2: Which is bigger, 1.09 or 1.1?
Working: Both have 1 whole. Tenths: 0 against 1. So 1.1 is bigger.
Answer: 1.1
Example 3: Order 2.07, 1.8, 1.078, 1.708, 1.07, largest first.
Working: 2.07 is the only one with 2 wholes. Then compare tenths: 1.8 (8), 1.708 (7), then 1.078 and 1.07 (both 0 tenths, 7 hundredths); 1.078 has 8 thousandths so it is bigger.
Answer: 2.07, 1.8, 1.708, 1.078, 1.07
Common mistakes and how to fix them
- Thinking longer decimals are bigger: 0.405 > 0.5. Compare tenths first. Length doesn't tell you size.
- Reading the digits after the point as a whole number ('45 is more than 5'). Say decimals digit by digit: 'nought point four five'. Use money or meters: 0.5 m is 50 cm, 0.45 m is 45 cm.
- Ignoring the whole number part. Always start from the left-most digit.
Activities to try at home
- Compare race times, long-jump distances or prices with decimals.
- Measure family members in meters to two decimal places and order them.
- Write decimals on cards and play 'higher or lower'.
Ideas for the classroom
- Use a place value chart with columns for ones, tenths, hundredths and thousandths.
- Place decimals on a zoomed-in number line, for example from 0.4 to 0.5.
- Ask students to create a 'tricky' set of decimals for a partner to order.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Is 0.5 bigger than 0.45?
Yes. 0.5 is 5 tenths (0.50), and 0.45 is only 4 tenths and 5 hundredths.
How should I choose this game for my learner?
Supports part of Common Core 5.NBT.A.3.b. This focused game does not cover the entire standard.
What is the US equivalent?
Common Core 5.NBT.A.3.b (Grade 5): compare two decimals to thousandths using >, = and <.