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Upper and lower bounds
Measurements are rounded, so calculations using them have a range of possible answers. Bounds find the extremes.
Bounds of a value
A length of 6.4 cm to 1 d.p. has lower bound 6.35 and upper bound 6.45.
Take half the rounding unit either side.
Take half the rounding unit either side.
Adding and multiplying
Largest sum or product: use both upper bounds.
Smallest: use both lower bounds.
Smallest: use both lower bounds.
Subtracting and dividing
Largest difference: upper − lower.
Largest quotient: upper ÷ lower.
To maximise a fraction, make the top big and the bottom small.
Largest quotient: upper ÷ lower.
To maximise a fraction, make the top big and the bottom small.
a = 9 to the nearest whole number and b = 2.5 to 1 d.p. Find the upper bound of a ÷ b.
- UB of a = 9.5, LB of b = 2.45
- 9.5 ÷ 2.45 = 3.877...
Answer: 3.88 (3 s.f.)
Bounds are half a unit either side. For the biggest answer: add or multiply uppers; subtract upper minus lower; divide upper by lower.
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