Ordering decimals

Ordering decimals: what children learn

Year 5 pupils learn to read, write, order and compare numbers with up to three decimal places. That means comparing numbers such as 0.5, 0.45, 0.405 and 0.054, which look similar but have quite different values.

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.

This topic covers the Year 5 statutory requirement in the National Curriculum in England (Number – fractions (including decimals and percentages)): pupils should be taught to “read, write, order and compare numbers with up to 3 decimal places”. Year 5 pupils are usually aged 9–10.

For families following US standards, the closest Common Core standard is 5.NBT.A.3.b, which is taught in Grade 5.

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

1. Compare the whole numbers first. 1.08 is bigger than 0.95 because 1 whole is more than 0 wholes.
2. 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.
3. 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.
4. 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

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 metres: 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 metres 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 pupils to create a 'tricky' set of decimals for a partner to order.

Printable worksheet

The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.

Open the printable worksheet

Frequently asked questions

Related topics

• Decimals on a number line (Year 4 maths) – Place tenths and hundredths on a number line. Free Year 4 maths game.
• Multiplying and dividing by 10, 100 and 1,000 (Year 5 maths) – Multiply and divide whole numbers and decimals by 10, 100 and 1,000. Free Year 5 maths game.
• Ordering numbers to 100 (Year 2 maths) – Put numbers to 100 in order, smallest or largest first. Free Year 2 maths game.
• Factors, multiples and primes (Year 5 maths) – Spot primes, factors and multiples in a timed quiz. Free Year 5 maths game.
• Square and cube numbers (Year 5 maths) – Fact sprint on square numbers to 12² and cube numbers to 5³. Free Year 5 maths game.
• Negative numbers (Year 5 maths) – Place positive and negative numbers from −10 to 10 on a number line. Free Year 5 maths game.

Back to Year 5 maths