Bounds, Rounding & Accuracy

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Corbett MathsUpper and lower bounds

Corbett MathsBounds calculations with formulas

GCSE Maths TutorBounds - Upper and Lower Bound Calculations | Grade 7-9 Maths Series | GCSE Maths Tutor

Key facts & methods

Rounding and error intervals

Error interval: the range of values a rounded number could have.
If x = 5.4 to 1 d.p.: error interval is 5.35 ≤ x < 5.45.
Lower bound = value that rounds up to the given figure. Upper bound = value just below the next rounded value.
The upper bound uses a strict inequality (<) because a value equal to the upper bound would round up.
Rounding to nearest 10: 250 could be anywhere from 245 ≤ x < 255.

Bounds in calculations

Maximum result: use the combination of bounds that gives the largest answer.
Minimum result: use the combination that gives the smallest answer.
For addition: max = UB + UB. Min = LB + LB.
For subtraction: max = UB − LB. Min = LB − UB.
For multiplication: max = UB × UB. Min = LB × LB.
For division: max = UB ÷ LB. Min = LB ÷ UB.
Always show which bounds you are using and state your answer clearly.

Exam questions — 5 questions · 12 marks · Edexcel 4MA1 style

2 marksError interval4MA1 Set 1 P1H Q2 style ✏️ No calculator

The height H cm of a table is measured as 72 cm correct to the nearest centimetre. Complete the error interval: _____ ≤ H < _____. (2 marks)

Hint: Nearest cm → bounds are ±0.5. Lower = 72 − 0.5. Upper = 72 + 0.5. Upper is strict (<) because 72.5 itself would round to 73.

+20 XP

3 marksBounds calculationGrade 7 Booklet Q3 🔢 Calculator

V = 250 correct to the nearest 5. R = 3900 correct to the nearest 100. The formula is I = V/R. Work out the lower bound for I. Give your answer to 3 d.p. Show your working. (3 marks)

Hint: For minimum of V/R: use minimum V ÷ maximum R. LB of V = 247.5 (nearest 5 → ±2.5). UB of R = 3950 (nearest 100 → ±50).

+30 XP

3 marksDensity bounds4MA1 style 🔢 Calculator

A block has mass M = 8.3 kg (correct to 1 d.p.) and volume V = 2.1 m³ (correct to 1 d.p.). Calculate the upper bound for the density D = M/V. Give your answer to 3 significant figures. (3 marks)

Hint: Maximum density = maximum mass ÷ minimum volume. UB of M = 8.35 (1 d.p. → ±0.05). LB of V = 2.05.

+30 XP

1 markEstimation4MA1 style

Estimate the value of (39.7 × 0.52) ÷ 1.97

A 10

B 1

C 100

D 20

Bounds, Rounding & Accuracy

Rounding and error intervals

Bounds in calculations

Module complete! 🎉