Understand the idea.
Always identify one whole
Identify one whole before reading a shaded diagram. If a complete hundred-grid is one whole, each of its one hundred equal squares represents , or . Counting shaded squares then tells you how many hundredths are shaded.
For thirty-six shaded squares, the shaded amount is . The unshaded squares complete the whole, but they are not part of the shaded count. Three complete rows give thirty hundredths and six more squares give another six hundredths.
Move between representations
A place-value chart sorts an amount into wholes, tenths and hundredths. A grid shows those parts as areas, while a number line shows the amount as a position. All three representations must use the same size for one whole.
On a number line from to with ten equal spaces, each jump is . Seven jumps reach . Count spaces from zero, rather than counting zero itself as the first jump.
See the method in action.
Read a grid
What decimal amount is shaded?
Worked solution
- 1
Set the value of one little square.
The whole grid consists of one hundred equal squares.
- 2
Count the shaded squares.
Fifty squares are shaded, so the chosen area is fifty hundredths of the whole.
- 3
Rename fifty hundredths as tenths.
Ten little squares make one tenth, so fifty squares make five tenths.
Use a chart
A chart contains 1 whole, 2 tenths and 5 hundredths. Write its decimal.
| Ones | Tenths | Hundredths |
|---|---|---|
| 1 | 2 | 5 |
Worked solution
- 1
Place the whole-number part before the point.
One complete unit belongs in the ones column.
- 2
Name the two fractional parts.
The chart gives two tenths and five hundredths, which occupy different columns.
- 3
Combine the chart entries.
The ones, tenths and hundredths entries form the decimal 1.25.
Try it yourself.
Check your understanding
A hundred-grid has 8 shaded squares. What decimal is shaded?
Show answer & reasoning
Eight shaded squares are eight hundredths: . The zero in the tenths column is needed because eight squares do not complete a full tenth.
Keep practising
6 worksheet questions · 8 marks
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 ↗