Higher only · bounds in calculations

Biggest answer?
Not always
big ÷ big.

choose your bounds
on purpose

every rounded number has —

Bounds

a lower and an upper bound

half a unit either side

step 1 of 4

Write every bound first

1. Nearest metre: half a metre either side.

2. 1 d.p.: 0.05 either side.

✓ Four bounds to choose from

d = 100 m nearest metre

99.5 ≤ d < 100.5

t = 12.4 s 1 d.p.

12.35 ≤ t < 12.45

step 2 of 4

Multiplying: big × big

1. Biggest area: both upper bounds.

2. Smallest area: both lower bounds.

✓ Adding works the same way

8.4 cm by 3.2 cm 1 d.p.

max = 8.45 × 3.25

= 27.4625 cm²

min = 8.35 × 3.15

step 3 of 4

Dividing: big ÷ small

1. Dividing by less gives more.

2. Max: upper ÷ lower. Min: lower ÷ upper.

✓ Subtracting works the same way

speed = d ÷ t

max = 100.5 ÷ 12.35

= 8.137…

min = 99.5 ÷ 12.45

= 7.991…

step 4 of 4

A suitable accuracy

1. Round both bounds the same way.

2. Use the accuracy where they agree.

✓ 8 m/s: both bounds round to 8

8.137… and 7.991…

2 s.f.   8.1 and 8.0 different

1 s.f.   8 and 8 agree

speed = 8 m/s

bounds in calculations —

+ and ×

max: upper with upper

− and ÷

max: upper with lower

Accuracy

where both bounds agree

Write every bound down
before you calculate.

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