Key Idea: Every real-world measurement is an approximation. This topic teaches you to round correctly (to decimal places or significant figures), measure how wrong an approximation is (percentage error), and find the range of values a rounded number could represent (upper and lower bounds).
Three things IB tests on this topic:
🎯 Rounding: d.p. vs s.f.
📐 Percentage error
Tip: Always divide by the exact (true) value vE — not the approximate one. Approx = 240, Exact = 256: ✓ ε = |240 − 256| ÷ 256 × 100 = 6.25% ✗ ε = |240 − 256| ÷ 240 × 100 = 6.67% ← wrong denominator
✏️ Worked examples
Round to significant figures
Round 0.048632 to 3 significant figures.
Step by step:
First significant figure: 4 (first non-zero digit)
2nd s.f.: 8, 3rd s.f.: 6
4th digit is 3 → do not round up
Answer: 0.0486
Final answer:
0.0486
Calculate percentage error
Estimated cost $240, actual cost $256. Find the percentage error.
Step by step:
vA = 240 (approximate), vE = 256 (exact)
ε = |240 − 256| ÷ 256 × 100
= 16 ÷ 256 × 100
= 6.25%
Final answer:
6.25%
Find bounds and max area
A box: length 15 cm, width 8 cm, each to the nearest cm. Find the maximum possible area.
Step by step:
Upper bound of length = 15.5 cm, upper bound of width = 8.5 cm
Maximum area = upper × upper = 15.5 × 8.5
= 131.75 cm²
Final answer:
Maximum area = 131.75 cm²
IB default: Give answers to 3 significant figures unless told otherwise. This applies after every GDC calculation. Percentage error: Identify the 'exact' or 'true' value — it goes in the denominator. The approximate value is what was estimated or measured. Bounds precision: The half-unit depends on the rounding used. Nearest cm → ±0.5 cm. Nearest 0.1 → ±0.05. Nearest 10 → ±5. Paper 1: Rounding questions are often 1–2 marks. Write clearly and show the digit you're rounding at.