Decimals on a number line: what children learn
The game uses two kinds of number line. One runs from 0 to 3 in tenths, with only the whole numbers labeled, for placing numbers such as 1.7. The other runs from 0 to 1 in hundredths, with bigger ticks for each tenth, for placing numbers such as 0.37. Because hundredths are so close together, being one hundredth out still counts on this line.
Supplemental practice placing decimal numbers on a line. This supports decimal understanding but does not cover all of 4.NF.C.6.
How to play
Move the marker to the right place on the number line, then press Check. You can drag, tap the line or use the arrow keys. Each game has 8 rounds. After you press Check, a green arrow shows the correct position if you were not quite right.
Step by step
- Work out what each step is worth. If one whole is split into 10 equal steps, each step is 0.1 (one tenth). If it is split into 100 steps, each is 0.01 (one hundredth).
- Find the whole number first. For 1.7, find 1, then count 7 tenths to the right.
- Use the tenths as signposts. For 0.37, find 0.3 (the third big tick), then count 7 small steps on towards 0.4.
- Check the size. 0.37 is less than a half (0.5), so it must be left of the middle.
Worked examples
Example 1: Put 2.4 on a 0 to 3 line in tenths.
Working: Find 2, then count 4 tenths to the right.
Answer: Four small steps after 2
Example 2: Put 0.82 on a 0 to 1 line in hundredths.
Working: Find 0.8 (the eighth big tick), then 2 small steps right.
Answer: Just past 0.8
Example 3: Put 0.05 on a 0 to 1 line in hundredths.
Working: Five hundredths is half of one tenth, so it is halfway between 0 and 0.1.
Answer: Between 0 and the first big tick
Common mistakes and how to fix them
- Thinking 0.5 is less than 0.37 because 5 is less than 37. Compare tenths first: 0.5 has 5 tenths, 0.37 has only 3.
- Treating every small tick as a tenth on a hundredths line. Count the small steps between 0 and 0.1. There are 10, so each is a hundredth.
- Reading 0.37 as 'nought point thirty-seven'. Say each digit after the point: 'nought point three seven'. This keeps the place values clear.
Activities to try at home
- Use money: $0.37 is 37¢, and $1.70 is one dollar and seventy cents.
- Use a meter stick or tape measure: 0.45 m is 45 cm.
- Look at race times or temperatures with decimals and put them in order.
Ideas for the classroom
- Use a 'zoom in' number line: show 0 to 1 in tenths, then zoom in between 0.3 and 0.4 to show hundredths.
- Use hundred squares: shade 37 squares to show 0.37.
- Connect this practice with dividing by 10 and 100 using a place-value chart.
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
What is the difference between tenths and hundredths?
A tenth is one whole split into 10 equal parts (0.1). A hundredth is one whole split into 100 equal parts (0.01). Ten hundredths make one tenth.
Why does being one hundredth out count as correct?
On a small screen, hundredths are only a few pixels apart, so the game accepts answers within one hundredth on that line. It shows the exact position afterwards.
Is the curriculum wording about 'hundreds' a mistake?
The published DfE text says 'decimal equivalents of any number of tenths or hundreds'. From the context and the rest of the program of study, this clearly means hundredths.
What is the US equivalent?
Common Core 4.NF.C.6 (Grade 4): use decimal notation for fractions with denominators 10 or 100, and locate decimals such as 0.62 on a number line.