Using a Calculator Efficiently and Accurately — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Work out each bracket first: numerator = 7.9, denominator = 1.2² = 1.44, then divide.
7.9 ÷ 1.44 = 5.4861… ≈ 5.49
Question 2
(a)Without brackets, the calculator applies the order of operations (BIDMAS) and divides only the 3 by the 2 first, giving a completely different, incorrect result rather than treating the whole top and bottom as one value each.
Brackets force the calculator to treat the full numerator and denominator as single values, avoiding an incorrect answer
Question 3
(a)√144 = 12, 3³ = 27, then add.
12 + 27 = 39
Question 4
(a)Work out the bracket first: 5.6−2.1=3.5, then multiply.
3.5 × 3.2 = 11.2
Question 5
(a)4.2² = 17.64, √50 ≈ 7.071, then subtract.
17.64 − 7.071 ≈ 10.6 (3 s.f.)
Question 6
(a)An estimate lets you sanity-check the calculator's answer, so a mis-keyed entry (wrong bracket placement, missed digit) is likely to be caught rather than accepted.
An estimate flags obviously wrong answers caused by a mis-typed calculation
Question 7
(a)This is almost always a rounding/floating-point display artefact from the calculator, not a genuinely non-integer answer; the true answer should be given as the whole number.
The calculator has a small rounding error — the answer should be written as 8
Question 8
(a)Add the bracket first (0.25), then find the reciprocal.
1 ÷ 0.25 = 4
Question 9
(a)Work inside the root first: 2.3²=5.29, +4=9.29, then take the square root.
√9.29 ≈ 3.05 (3 s.f.)
Question 10
(a)Work out the bracket and the power first: 7−2.5=4.5, 1.5²=2.25, then divide.
4.5 ÷ 2.25 = 2
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