Significant figures count from the first non-zero digit: 0.04726 is 0.0473 to 3 s.f. A rounded value has an error interval: if x=7 to the nearest whole number, then 6.5≤x<7.5.
Find the last digit you keep, then look at the next digit: 5 or more rounds up.
For an error interval, take half the rounding unit below and above.
The lower bound uses ≤ and the upper bound uses <.
Watch out Rounding to 1 decimal place and to 1 significant figure are different: 0.0638 is 0.1 to 1 d.p. but 0.06 to 1 s.f.
See it worked
Worked exampleNon-calculator·3 marks
Round each number as instructed.
(a) Round 3.4762 to 2 decimal places.
(b) Round 48350 to 2 significant figures.
(c) Round 0.006072 to 1 significant figure.
(a) The second decimal digit is 7; the next digit, 6, is 5 or more, so round up: 3.48.
(b) The first two significant figures are 4 and 8; the next digit is 3, so round down. Keep the place value with zeros: 48000.
(c) The zeros after the point are not significant. The first significant figure is 6; the next digit is 0, so 0.006.
Answer (a) 3.48; (b) 48000; (c) 0.006
Your turn
Question 1Non-calculator·1 mark
Round 0.007846 to 2 significant figures.
Question 2Non-calculator·1 mark
A positive number x is truncated to one decimal place. The result is 5.8. Which interval describes x?
Question 3Non-calculator·4 marks
A mass is recorded as 3.70 kg, rounded to the nearest 0.01 kg.
(a) Write the error interval for the actual mass m in kg.
(b) A delivery contains 8 such bags. Find the upper bound for their total mass.
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