Practice 1
Answer & reasoning
3.6 · Three tenths become three ones; six hundredths become six tenths.
Why multiplying by ten changes each place value
Track what happens to each digit’s value instead of appending a zero to a decimal.
Try the practice questionsStart with this question
Why is 0.24 × 10 equal to 2.4, not 0.240?
The key idea: Each digit represents ten times as much: two tenths become two ones, and four hundredths become four tenths.
Make the idea visible
- Read 0.24 as two tenths plus four hundredths.
- Multiply each part by ten. Ten copies of two tenths make two ones; ten copies of four hundredths make four tenths.
- Combine two ones and four tenths to make 2.4. The decimal point continues to mark the boundary between ones and tenths.
- Check with an estimate: ten copies of about one quarter should be about two and a half, so 2.4 is sensible.
A useful error to discuss
A learner might say: Multiplying by ten always means adding a zero at the end.
A final zero in 0.240 does not change its value. Multiplication by ten changes the amount. Track the value represented by each digit.
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
20.7 · The zero keeps the empty ones place in the result.
Practice 3
Answer & reasoning
5 · One hundred copies of five hundredths make five wholes.
Independent check
Answer & reasoning
0.04 · Four thousandths become four hundredths.
Explain a new situation
Explain why 3.2 × 100 can be found by multiplying by ten twice.
Discuss the explanation
100 = 10 × 10. Each multiplication makes the value ten times as large: 3.2 becomes 32, then 320.
Materials for your group
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.
Choose the next step
If the learner appends zeros, compare 0.24 with 0.240 in the chart. Ask them to build ten copies before using a shortcut.
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