Practice 1
Answer & reasoning
0.06 · Six hundredths is 6/100; the tenths place is empty.
What does the zero in 0.04 do?
Keep tenths and hundredths in their places. Use a place-value chart to distinguish 0.4, 0.04 and 0.004.
Try the practice questionsStart with this question
A learner writes four hundredths as 0.4. What has changed?
The key idea: 0.04 is four hundredths. Writing 0.4 makes the 4 worth four tenths, ten times as much.
Make the idea visible
- Name one whole before comparing any models. A tenth is one of ten equal parts; a hundredth is one of one hundred equal parts of that same whole.
- Write 0.4 and 0.04 in a chart with the decimal point between ones and tenths. Read them as four tenths and four hundredths.
- Rename four tenths as forty hundredths. Compare forty hundredths with four hundredths: the first amount is ten times the second.
- Contrast 0.04 with 0.040. Adding an empty thousandths place at the end does not move the 4; removing the tenths placeholder does.
A useful error to discuss
A learner might say: A zero after the decimal point can always be removed.
Read the unit named by each column. In 0.04, the zero holds the empty tenths place so the 4 stays in the hundredths column. Removing that zero moves the 4 into another place.
Practise, then check
Try the first three questions with the model. Try the final check without help. A correct value is a starting point: explain how your units or drawing support it.
Practice 2
Answer & reasoning
0.07 · The 7 is in the hundredths column.
Practice 3
Answer & reasoning
10 · Eight tenths is eighty hundredths.
Independent check
Answer & reasoning
0.005 · Keep empty tenths and hundredths places before the 5.
Explain a new situation
Explain why 0.09 and 0.090 are equal but 0.09 and 0.9 are not.
Discuss the explanation
The final zero adds no thousandths. Removing the zero before the 9 changes nine hundredths to nine tenths.
Materials for your group
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Choose the next step
If the learner names a digit without a unit, return to the chart. If the places are secure, compare decimals with different written lengths.
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