The idea, step by step
Always identify one whole
A shaded diagram only has a decimal meaning once we know what counts as one whole. In a hundred-grid the entire grid is one whole, so each little square is one hundredth.
Thirty-six shaded squares mean thirty-six hundredths, or 0.36. Do not count the unshaded squares as the shaded amount.
Move between representations
A place-value chart shows how many wholes, tenths and hundredths an amount contains. A number line shows its position and how it compares with other amounts.
On a line divided into tenths, the seventh jump after zero is 0.7. The ten equal spaces fill one whole.
A common trap
Calling one shaded square 0.1 when the full hundred-grid is one whole.
Instead: There are one hundred equal squares in the whole. One square is 0.01; a row of ten squares is 0.1.
See the thinking
Read a grid
What decimal amount is shaded?
- The complete grid represents one whole.
- There are fifty shaded squares out of one hundred.
- Fifty hundredths is five tenths.
Use a chart
A chart contains 1 whole, 2 tenths and 5 hundredths. Write its decimal.
| Ones | Tenths | Hundredths |
|---|---|---|
| 1 | 2 | 5 |
- Put each count into its correct column.
- The whole-number digit goes before the point; tenths and hundredths go after it.
Check your understanding
A hundred-grid has 8 shaded squares. What decimal is shaded?
Show answer
Each little square is one hundredth, so eight squares are eight hundredths.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Write the decimal shown by the shaded grid.1 mark
- A strip is split into 10 equal pieces. Seven are shaded. Write the decimal.1 mark
- Write the decimal in the place-value chart.1 mark
Ones Tenths Hundredths 2 1 4 - How many squares should be shaded to show 0.6 on a hundred-grid?1 mark
- On a blank hundred-grid, shade an amount equal to 0.08.2 marks
- Two full grids and four tenths of another equal grid are shaded. Write the decimal and explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write the decimal shown by the shaded grid.1 mark
Twenty-seven of one hundred squares are shaded.
- A strip is split into 10 equal pieces. Seven are shaded. Write the decimal.1 mark
Seven of ten equal parts are seven tenths.
- Write the decimal in the place-value chart.1 mark
Ones Tenths Hundredths 2 1 4 Two wholes, one tenth and four hundredths make 2.14.
- How many squares should be shaded to show 0.6 on a hundred-grid?1 mark
Six tenths equal sixty hundredths.
60 squares. - On a blank hundred-grid, shade an amount equal to 0.08.2 marks
The full grid is one whole; each small square is one hundredth.
Any 8 of the 100 squares shaded. - Two full grids and four tenths of another equal grid are shaded. Write the decimal and explain.2 marks
The two full grids make 2 wholes; the extra part is 4 tenths.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Tenths/hundredths; representations; notation; fraction connections.
Official curriculum source ↗