Practice 1
Answer & reasoning
0.8 · 0.84 is below the midpoint 0.85.
Round decimals by finding the nearest endpoint
Use two neighbouring tenths and their midpoint to explain rounding, including values close to the next whole.
Try the practice questionsStart with this question
Why does 0.96 round to 1.0 to the nearest tenth?
The key idea: Its neighbouring tenths are 0.9 and 1.0. It is 0.04 away from 1.0 and 0.06 away from 0.9, so 1.0 is nearer.
Make the idea visible
- To round to the nearest tenth, identify the tenth immediately below and the tenth immediately above the number.
- Locate their midpoint. Between 0.9 and 1.0, the midpoint is 0.95.
- Place 0.96 beyond that midpoint, nearer to 1.0. Record 1.0 so the requested tenths place remains visible.
- For nonnegative midpoint cases in these tasks, use the classroom convention of rounding up. State that convention when the distances are equal.
A useful error to discuss
A learner might say: Rounding only changes a digit and can never cross a whole-number boundary.
Name the two surrounding multiples of the required place. The upper tenth after 0.9 is 1.0. Use distance to choose, rather than attaching a rule to an isolated 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
1.3 · 1.27 is closer to 1.3 than to 1.2.
Practice 3
Answer & reasoning
3.0 · 2.95 is halfway between 2.9 and 3.0; the stated convention selects 3.0.
Independent check
Answer & reasoning
1.00 · The neighbouring hundredths are 0.99 and 1.00.
Explain a new situation
Explain why 0.949 rounds to 0.9 to the nearest tenth even though its final digit is 9.
Discuss the explanation
The whole number 0.949 is below the midpoint 0.95. The last digit alone does not choose the nearest tenth.
Materials for your group
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Choose the next step
If the learner rounds the final digit first, return to the original number on the line. Avoid repeated rounding through intermediate places.
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