Bounds in calculations

The Maths Habit

Find the lower and upper bounds.

  1. A path is 70 m, to the nearest 10 m.

    65 m and 75 m

  2. A box is 1.5 kg, to 1 decimal place.

    1.45 kg and 1.55 kg

  3. A crowd is 3000 people, to the nearest 100.

    2950 and 3050

A rug is 2 m by 3 m, each to the nearest metre.

Could its area be more than 6 m2?

Yes: it could be nearly 2.5 m by 3.5 m, which is nearly 8.75 m2

Lower bound
The smallest value a rounded number could have been.
Upper bound
The value a rounded number must have been below.

9 cm, to the nearest cm

9 cmlengthlower boundupper bound

Two rods are 7.3 cm and 2.6 cm, each to 1 decimal place.
Find the least possible total length.

7.3 cmfirst rodlower boundupper bound
2.6 cmsecond rodlower boundupper bound

A rectangle is 10 cm by 6 cm, each to the nearest cm. Find the greatest possible area.

greatest area: use both upper bounds
9.510 cm10.5lower boundlengthupper bound
5.56 cm6.5lower boundwidthupper bound
Greatest area =10.5×6.5=68.25 cm2

A rectangle is 7 cm by 3 cm, each to the nearest cm. Find the greatest possible area.

6.57 cm7.5lower boundlengthupper bound
2.53 cm3.5lower boundwidthupper bound
Greatest area =7.5×3.5=26.25 cm2

A rectangle is 10 cm by 6 cm, each to the nearest cm. Find the greatest possible area.

greatest area: use both upper bounds
9.510 cm10.5lower boundlengthupper bound
5.56 cm6.5lower boundwidthupper bound
Greatest area =10.5×6.5=68.25 cm2

A rectangle is 11 cm by 4 cm, each to the nearest cm. Find the greatest possible area.

10.511 cm11.5lower boundlengthupper bound
3.54 cm4.5lower boundwidthupper bound
Greatest area =11.5×4.5=51.75 cm2

To make the answer to a subtraction as big as possible, which bounds do you use?

Upper bound − lower bound

Each is to the nearest whole number.
Find the greatest possible a − b.

a = 7     b = 4 4

A runner covers 300 m, to the nearest 10 m, in 40 s, to the nearest second. Find the greatest possible speed, to 2 decimal places.

greatest speed: greatest distance ÷ least time
295300 m305lower bounddistanceupper bound
39.540 s40.5lower boundtimeupper bound
Greatest speed =305÷39.5=7.72 m/s

A runner covers 150 m, to the nearest 10 m, in 20 s, to the nearest second. Find the greatest possible speed, to 2 decimal places.

145150 m155lower bounddistanceupper bound
19.520 s20.5lower boundtimeupper bound
Greatest speed =155÷19.5=7.95 m/s

A runner covers 300 m, to the nearest 10 m, in 40 s, to the nearest second. Find the greatest possible speed, to 2 decimal places.

greatest speed: greatest distance ÷ least time
295300 m305lower bounddistanceupper bound
39.540 s40.5lower boundtimeupper bound
Greatest speed =305÷39.5=7.72 m/s

A runner covers 250 m, to the nearest 10 m, in 30 s, to the nearest second. Find the least possible speed, to 2 decimal places.

245250 m255lower bounddistanceupper bound
29.530 s30.5lower boundtimeupper bound
Least speed =245÷30.5=8.03 m/s

Bounds in calculations worksheet, page 1

Bounds in calculations worksheet, page 2

Answer sheet

  1. p = 4.2 and q = 1.8, each correct to 1 decimal place. Work out the upper bound of p ÷ q, to 2 decimal places.

    2.43

  2. A lift can carry 600 kg, to the nearest 10 kg. Each crate has a mass of 50 kg, to the nearest kg. What is the greatest number of crates that is certain to be safe?

    11

  1. A rectangle is 8 cm by 5 cm, each to the nearest cm. Find the least possible area.

    33.75 cm2

  2. A 50 cm piece is cut from a 120 cm plank, both to the nearest 10 cm. Find the greatest possible length left.

    80 cm

  3. A car travels 200 m, to the nearest 10 m, in 16 s, to the nearest second. Find the least possible speed. Give your answer to 2 decimal places.

    11.82 m/s
Exit tickets to print