Estimation & approximation

By writing each number correct to 1 significant figure, find an estimate for this calculation. 3.81 × 19.8

A solid steel cube has a mass of 1.05 kg. The density of the steel is 7.9 g/cm³.

Orla says,

The length of one side of the cube is approximately 10 cm.

Use estimation to decide if Orla’s statement is reasonable. Show how you decide.

Orla’s statement is........ because........

By rounding each value to one significant figure, estimate the cost of 4.9 kg of carrots at 73p per kg.

A student works out an estimate for this calculation.

13.7 + 1.28

Their method is to:

• round each number correct to the same number of significant figures and

• work out the approximation.

The student writes

What error has the student made in using their method?

The table shows how much Amaya earns per hour.

One week Amaya works for 40 hours between Monday and Friday and then for hours on Saturday.³⁴

Amaya says

I will earn at least £900 for my work this week.

By rounding each value to the nearest integer, use estimation to show that Amaya may be

correct.

Give one reason why your working in part (a) shows that Amaya can be certain of earning at least £900 for her work in this week.

A bronze ornament has a volume of 198 cm³. The density of bronze is 8.9 g/cm³.

By rounding each value correct to one significant figure, work out an estimate for the mass of the bronze ornament.

Four apples cost £1.80.

Find the cost of five of these apples.

By rounding each value to one significant figure, estimate the cost of 8.2 kg of bananas at 73p per kg. Give your answer in pounds.

By writing each number correct to 1 significant figure, find an estimate for this calculation.

A block made of iron is in the shape of a cuboid. The block is 3.1 cm by 4.9 cm by 2.2 cm. The density of iron is 7.87 g / cm³. Sam thinks that the mass of the block is about 2.4 kg.

Use estimation to decide if Sam’s answer is reasonable. Show how you decide.

Sam’s answer is........ because........

By writing each number correct to 1 significant figure, find an estimate for 79.8 × 3.1.

Jamie works out 79.8 × 3.1 on a calculator. Jamie’s answer is 2473.8.

Do you think Jamie has used their calculator correctly? Explain why.

Force is measured in newtons (N). A force of 198.5 N is applied to a rectangular surface of length 4.9 cm and width 4.1 cm.

Work out an estimate of the pressure, in N / cm², applied to this rectangular surface.

[The formula for pressure is: Pressure =

Force is measured in newtons (N). A force of 198.5 N is applied to a rectangular surface of length 4.9 cm and width 4.1 cm.

Work out an estimate of the pressure, in N / cm², applied to this rectangular surface. [The formula for pressure is: Pressure =

Show that Nina’s answer is 64.

Calculate the error in her estimated answer as a percentage of the exact answer.

Work out.

Give your answer in its simplest form.

By writing each number correct to 1 significant figure, use estimation to show that

By rounding each value to one significant figure, estimate the cost of 3.9 kg of apples at 87p per kg.

Work out.

8 ÷ 0.4

By writing each number correct to 1 significant figure, find an estimate for this calculation.

By writing each number correct to 1 significant figure, find an estimate for this calculation.

She got an answer of 19.5, correct to 3 significant figures.

Write each number correct to 1 significant figure to decide if Asha’s answer is reasonable.

Earth and Pluto go around the Sun. Their distance to the Sun varies.

The table shows the closest distance that Earth and Pluto get to the Sun.

Show that the closest distance of Pluto to the Sun is roughly 30 times the closest distance of

Earth to the Sun.

Give a reason why we cannot use this information to say

The distance of Pluto to the Sun is always 30 times the distance of Earth to the Sun.

She got an answer of 19.5, correct to 3 significant figures.

Write each number correct to 1 significant figure to decide if Asha’s answer is reasonable.

Work out.

1 + 4 ÷ 2

2 + 5 × (8 - 4)

Evaluate.

2⁵

Estimate the value of

Grapes cost £2 per kilogram.

Calculate the cost of 380 g of grapes.

Ruth buys 19 identical tickets for £280.25.

Estimate the cost of one ticket. Show your working.