Rounding, estimating and checking
Accuracy is a judgement, not a rule. A carpenter rounds to the nearest millimetre, an astronomer to the nearest million kilometres, and both are being precise for their purpose.
Part of your national curriculum
- Number: Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers
Lesson overview
What you'll learn in this lesson
Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers
Key learning points
- • Significant figures
- • Estimating a calculation
- • Measurement bounds
- • Rounding only at the end
This lesson at a glance
- 28 minutes
- 21 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 21
Visual introductionPicture this
Rounding, estimating and checking
Accuracy is a judgement, not a rule. A carpenter rounds to the nearest millimetre, an astronomer to the nearest million kilometres, and both are being precise for their purpose.
In a nutshell
Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers
Learning cycle
Part 2 of 21
Learning cycle 1 of 2
Part 1 · Significant figures
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 21
Learn
Significant figures
The first significant figure is the first non-zero digit. In 0.004072 the first significant figure is 4, so to 2 s.f. the number is 0.0041. Significant figures suit measurements of very different sizes, while decimal places suit money and quantities on a shared scale.
Reset break
Part 4 of 21
Pause
That's sitting 1 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 21
Learn
Estimating a calculation
Round every number to 1 s.f. and calculate mentally. For (48.7 × 6.1) ÷ 0.52 estimate (50 × 6) ÷ 0.5 = 300 ÷ 0.5 = 600. If your calculator gives 57 or 5,700 you have made a place-value error, and the estimate has done its job.
Quick check
Part 6 of 21
Quick check
Part 7 of 21
Reset break
Part 8 of 21
Pause
That's sitting 2 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 21
Learning cycle 2 of 2
Part 2 · Measurement bounds
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 21
Learn
Measurement bounds
A length recorded as 12.4 cm to 1 d.p. lies between 12.35 cm and 12.45 cm: half a unit either side. Every measurement carries this uncertainty, so quoting an answer to eight decimal places from data measured to the nearest millimetre claims precision the data cannot support.
Explore the idea
Part 11 of 21
Learn
Rounding only at the end
Rounding partway through a multi-step calculation makes small errors grow. Keep full accuracy in your working, use the calculator memory, and round once at the final step, stating the accuracy you used.
Reset break
Part 12 of 21
Pause
That's sitting 3 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 13 of 21
Quick check
Part 14 of 21
Explore the idea
Part 15 of 21
Worked example
Worked answer: estimate (48.7 × 6.1) ÷ 0.52 and comment on your estimate (3 marks)
Rounding to 1 s.f. gives (50 × 6) ÷ 0.5 (1). The numerator is 300 and dividing by 0.5 doubles it, giving an estimate of 600 (1). The estimate is slightly high because 48.7 and 0.52 were both rounded in directions that increase the result, so the true answer, 571 to 3 s.f., is a little lower (1).
Reset break
Part 16 of 21
Pause
That's sitting 4 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 17 of 21
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 18 of 21
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Keep full ____ in your working, use the calculator memory, and round once at the final step, stating the accuracy you used.
Challenge round
Part 19 of 21
Game · Recall cards
Round 462 to the nearest hundred.
Card 1 of 4
Mastery quiz
Part 20 of 21
Marked quiz
End of lesson quiz: Rounding, estimating and checking
4 questions, marked with the reasoning shown. No timer.
1. Round 462 to the nearest hundred.
2. Estimate 38 × 21 by rounding to the nearest 10.
3. Why use estimation before an exact calculation?
4. 0.004072 to 2 significant figures is
Lesson round-up
Part 21 of 21
Lesson round-up
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Ask LunaPart 1 of 21 · Watch & discover
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Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers