Section A · Step 0
Rounding to Significant Figures
Method: The first significant figure is the first digit that is not zero, reading from the left. Zeros before it never count; zeros between other digits do count. To round to n s.f., count n digits from the first significant figure, look at the next digit (5 or more rounds up), and then fill any empty places before the decimal point with zeros so the number keeps its size.
Example: 0.002 58 to 2 s.f. → the significant figures start at the 2 → 0.0026. 71 460 to 2 s.f. → 71|460 → 71 000 (not 71: the zeros hold the place value).
Q1
How many significant figures does 0.0305 have?
1 mark
Q2
Round 4782 to 2 significant figures.
1 mark
Q3
Round 0.04671 to 2 significant figures.
1 mark
Q4
Round 36.52 to 1 significant figure.
1 mark
Q5
Which is 58 347 correct to 2 significant figures?
1 mark
Q6
Which is 0.3996 written correct to 3 significant figures?
1 mark
SIGNIFICANT FIGURES — SECTION SCORE
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Section B · Step 1
Find the Unit of Rounding
Why this step: every bound starts from the unit of rounding — the size of the jumps between possible rounded answers. Nearest 1000 → 1000. Nearest 10 → 10. Nearest whole number → 1. One decimal place → 0.1.
For significant figures: look at the last significant figure of the rounded number and ask which place it is in. Example: 3700, correct to 2 s.f. → the 2nd significant figure is the 7, in the hundreds → unit 100. Example: 0.058, correct to 2 s.f. → the 8 is in the thousandths → unit 0.001.
Q7
A length is rounded correct to 2 decimal places. What is the unit of rounding?
1 mark
Q8
A height is given as 5300 m, correct to 2 significant figures. What is the unit of rounding?
1 mark
m
Q9
A mass is given as 0.62 kg, correct to 2 significant figures. What is the unit of rounding?
1 mark
kg
Q10
A distance is given as 80 000 km, correct to 1 significant figure. What is the unit of rounding?
1 mark
km
Q11
A time is given as 7.0 seconds, correct to 2 significant figures. What is the unit of rounding?
1 mark
s
THE ROUNDING UNIT — SECTION SCORE
0/5
Section C · Steps 2 & 3
Measurements: Half a Unit Either Side
Method for a measurement (length, mass, time, area …), which can have any number of decimal places:
- Find the unit of rounding.
- Halve it.
- Lower bound = rounded value − half. Upper bound = rounded value + half. Write lower ≤ x < upper.
Example: A parcel is 850 g, to the nearest 10 g. Unit 10 → half 5 → 850 − 5 = 845 and 850 + 5 = 855 → 845 ≤ m < 855. The < sign is there because 855 g itself would round up to 860 g.
Reading the inequality: x stands for the exact value, and it sits in the middle. Read it from the middle outwards: 845 ≤ m means “m is 845 or more”, and m < 855 means “m is less than 855”. So 850 fits (850 is 845 or more, and less than 855), and so do 845 and 854.99, but 855 does not. A whole-number or one-decimal-place range uses ≤ on both sides, such as 4.5 ≤ x ≤ 5.4: x is 4.5 or more and 5.4 or less.
Bounds Explorer — type any rounded value, then drag the orange marker
Q12
A suitcase weighs 62 kg, correct to the nearest kg. What is the lower bound of its mass?
1 mark
kg
Q13
The circumference of a pond is 1560 cm, correct to the nearest 10 cm. What is the upper bound?
1 mark
cm
Q14
A runner’s time is 7.3 seconds, correct to 1 decimal place. What is the lower bound?
1 mark
s
Q15
A pole is 2.46 m long, correct to 2 decimal places. What is the upper bound?
1 mark
m
Q16
The mean height of a netball team is 172 cm, correct to the nearest cm. Which inequality shows the range of values the mean height could have?
1 mark
Q17
The area of a soccer pitch is 7200 m², correct to the nearest 100 m². What is the lower bound of the area?
1 mark
m²
HALF A UNIT — SECTION SCORE
0/6
Section D
Bounds with Significant Figures
Method: exactly the same three steps as Section C. The only extra work is Step 1: use Section B to turn “correct to n s.f.” into a unit of rounding first.
Example: A road is 2300 m long, to 2 s.f. → the 3 is in the hundreds, so unit 100 → half 50 → 2250 ≤ L < 2350. A bag of sugar is 0.6 kg, to 1 s.f. → unit 0.1 → half 0.05 → 0.55 ≤ m < 0.65.
Q18
A lorry has a mass of 4700 kg, correct to 2 significant figures. What is the lower bound of its mass?
1 mark
kg
Q19
A bottle holds 0.38 litres, correct to 2 significant figures. What is the upper bound?
1 mark
litres
Q20
A satellite travels 60 000 km, correct to 1 significant figure. What is the upper bound of the distance?
2 marks
km
Q21
A screw is 5.0 cm long, correct to 2 significant figures. What is the lower bound of its length?
2 marks
cm
Q22
A pill contains 0.09 g of medicine, correct to 1 significant figure. Which inequality shows the range of possible masses?
1 mark
BOUNDS WITH S.F. — SECTION SCORE
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Section E
Which Kind of Number Was Rounded?
Step 0 for every bounds question: read what kind of number was rounded. The lower bound is found the same way every time; it is the upper bound that changes. The table shows three numbers that all round to 20, to the nearest 10.
| What was rounded | It can be | Range | Upper bound |
|---|---|---|---|
| A whole number (a count: people, pages) | 15, 16, …, 24 | 15 ≤ x ≤ 24 | 24 — 25 rounds to 30 |
| A number with one decimal place | 15.0, 15.1, …, 24.9 | 15 ≤ x ≤ 24.9 | 24.9 — 25.0 rounds to 30 |
| A measurement or any decimal | anything from 15 up to 24.999… | 15 ≤ x < 25 | 25 — x gets close but never equals it |
The ≤ or < rule:
- The lower bound is always included, so it always uses ≤.
- The upper bound is included (≤) only when you can list the values: whole numbers, or numbers with one decimal place.
- For a measurement or any decimal, the upper bound is the halfway point and is not included, so it uses <.
Q23
A whole number is rounded to the nearest 10. The answer is 30. What is the upper bound?
1 mark
Q24
A number with one decimal place is rounded to the nearest whole number. The answer is 6. What is the upper bound?
1 mark
Q25
A plank is 6 m long, correct to the nearest metre. What is the upper bound of its length?
1 mark
m
Q26
A number is rounded to the nearest 100, giving 700. Its upper bound is 749. What kind of number was rounded?
1 mark
Q27
A number with one decimal place is rounded to the nearest 10. The answer is 50. What is the upper bound?
2 marks
Q28
The number of seats in a theatre is 2000, correct to 2 significant figures. What is the largest possible number of seats?
2 marks
seats
WHICH KIND OF NUMBER? — SECTION SCORE
0/8
Section F
Mini Test
No method box here. Try these like a real test: for each one, write down Step 0 (what kind of number?), Step 1 (the unit), Step 2 (half of it) before you answer. Use the hints only if you are stuck.
Q29
The crowd at a concert was 38 000 people, correct to the nearest 1000. What is the upper bound of the crowd?
1 mark
people
Q30
A melon has a mass of 0.75 kg, correct to 2 significant figures. What is the lower bound of its mass?
1 mark
kg
Q31
A decimal number is rounded to the nearest 10, giving 160. Which inequality shows the range of values it could have?
1 mark
Q32
A swimmer’s time is 12.0 seconds, correct to 3 significant figures. What is the upper bound of the time?
2 marks
s
Q33
A decimal number, which could have any number of decimal places, is rounded to 1 significant figure. The answer is 0.4. What is the lower bound?
2 marks
Q34
A rope is 8 m long, correct to the nearest metre. Which of these could not be its exact length?
1 mark
MINI TEST — SECTION SCORE
0/8
0%
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