Rounding, bounds and standard form
Real measurements are never exact. Bounds tell you how far a rounded value could be from the truth, and standard form keeps very large and very small numbers manageable.
Lesson overview
What you'll learn in this lesson
Apply number operations, accuracy and standard form to solve GCSE-style problems.
Key learning points
- • Significant figures and estimation
- • Upper and lower bounds
- • Standard form
This lesson at a glance
- 30 minutes
- 20 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 20
Visual introductionPicture this
Rounding, bounds and standard form
Real measurements are never exact. Bounds tell you how far a rounded value could be from the truth, and standard form keeps very large and very small numbers manageable.
In a nutshell
Apply number operations, accuracy and standard form to solve GCSE-style problems.
Learning cycle
Part 2 of 20
Learning cycle 1 of 2
Part 1 · Significant figures and estimation
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 20
Learn
Significant figures and estimation
The first significant figure is the first non-zero digit. To estimate a calculation, round each value to one significant figure and work it out mentally: 38.7 × 6.2 ÷ 0.48 becomes 40 × 6 ÷ 0.5 = 480. Examiners award the method, so show the rounded values.
Reset break
Part 4 of 20
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 20
Learn
Upper and lower bounds
A length given as 24 cm to the nearest centimetre lies between 23.5 cm and 24.5 cm. For a sum or product, the maximum uses both upper bounds. For a subtraction or division, the maximum uses the upper bound of the first and the lower bound of the second — a rule worth memorising.
Quick check
Part 6 of 20
Quick check
Part 7 of 20
Reset break
Part 8 of 20
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 20
Learning cycle 2 of 2
Part 2 · Standard form
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 20
Learn
Standard form
A number in standard form is written as A × 10ⁿ, where 1 ≤ A < 10. Multiply by adding the indices and dividing by subtracting them, then adjust so A sits back in range: 40 × 10⁵ must be rewritten as 4 × 10⁶ before it counts as standard form.
Quick check
Part 11 of 20
Reset break
Part 12 of 20
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 20
Explore the idea
Part 14 of 20
Worked example
Worked answer: a rectangle measures 8.4 cm by 5.2 cm, each to 1 d.p. Find the upper bound of its area (3 marks)
The upper bounds of the sides are 8.45 cm and 5.25 cm, since each measurement is within 0.05 cm of the stated value (1). Area is a product, so the upper bound uses both upper bounds: 8.45 × 5.25 (1) = 44.3625 cm² (1). Using 8.5 and 5.3 is the common error: those are bounds to the nearest 0.1, not the nearest 0.05.
Challenge round
Part 15 of 20
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
Reset break
Part 16 of 20
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 20
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
A ____ in standard form is written as A × 10ⁿ, where 1 ≤ A < 10.
Multiply by adding the indices and dividing by subtracting them, then adjust so A sits back in range: 40 × 10⁵ must be rewritten as 4 × 10⁶ before it counts as ____ form.
Challenge round
Part 18 of 20
Game · Recall cards
0.00482 to 2 significant figures is
Card 1 of 4
Mastery quiz
Part 19 of 20
Marked quiz
End of lesson quiz: Rounding, bounds and standard form
4 questions, marked with the reasoning shown. No timer.
1. 0.00482 to 2 significant figures is
2. A mass of 60 kg to the nearest kg has lower bound
3. (3 × 10⁵) × (4 × 10³) equals
4. For a division, the upper bound uses
Lesson round-up
Part 20 of 20
Lesson round-up
Ready when you are
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Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 20 · Watch & discover