Rounding

Calculate.

Give your answer correct to 3 significant figures.

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

Round 4352 to the nearest hundred.

Round £5.3725 to the nearest penny.

A decorator works out how much to charge for some painting.

The decorator

• rounds up the area to be painted to the next 10 m²

• then charges £65 for every 10 m².

Work out how much the decorator charges for painting an area of 74 m².

Calculate.

Give your answer correct to 3 significant figures.

The circumference of a circle is 17 cm.

Calculate the diameter of the circle. Give your answer correct to 1 decimal place.

Insert two of these symbols +, -, × or ÷ to make this calculation correct.

5........ (3........ 1) = 20

Calculate

Give your answer correct to 3 significant figures.

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?

Sam eats 30% of a 600 g pack of cereal every day.

Sam has no cereal left. The cereal is no longer sold in 600 g packs. Instead, the cereal is now sold in 400 g packs.

Sam wants to continue to eat the same amount of cereal every day.

Work out the minimum number of 400 g packs of cereal that Sam must buy to have enough for 7 days. You must show your working.

Work out.

₃ 19.5⁴ - 18²

Write your answer correct to 4 significant figures.

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.

Work out.

₃ 19.5⁴ - 18²

Write your answer correct to 4 significant figures.

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.

Round 3648 to the nearest hundred.

Round £3.2875 to the nearest penny.

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.

A number, r, is 6.2 when rounded correct to 2 significant figures. A number, h, is 6.2 when truncated to 1 decimal place.

Write down a possible value of r that will definitely be less than all possible values of h.

Write down a possible value of h that will definitely be greater than all possible values of r

Write down a possible value of r and a possible value of h such that r is greater than h.

(c) r =........ and h =........

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

Calculate.

Give your answer correct to 3 significant figures.

Calculate.

Give your answer correct to 3 significant figures.

Rowan invests £4000 at a rate of 3.5% per year compound interest.

Calculate the value of Rowan’s investment after 5 years. Give your answer correct to the nearest penny.

The table below shows the approximate population of three countries in 2020.

Calculate the approximate total population of Kiribati and Tuvalu in 2020. Give your answer in standard form, correct to 3 significant figures.

Show that in 2020 the population of China was approximately 120 000 times the population

of Tuvalu.

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.

The diagram shows two right-angled triangles that are joined together.

All measurements are given accurate to 2 significant figures.

8.3 cm Not to scale

Work out the value of x. Give your answer correct to an appropriate degree of accuracy. You must show your working.

A machine can dig, on average, 2 cm of tunnel each minute. It operates 24 hours each day.

Work out how many days it should take to dig a tunnel of length 3.5 km. Give your answer to the nearest day.

The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.

How would this affect your answer to part (a) ?

The diagram shows Kai’s garden. It is in the shape of a right-angled triangle.

Kai is going to spread grass seed on the garden.

• A bag of grass seed covers an area of 35 m².

• Each bag of grass seed costs £8.99.

Kai can only buy whole bags of grass seed. Kai buys the least number of bags needed for the garden.

Calculate the cost of buying the bags of grass seed that Kai needs. You must show your working.

A machine can dig, on average, 2 cm of tunnel each minute. It operates 24 hours each day.

Work out how many days it should take to dig a tunnel of length 3.5 km. Give your answer to the nearest day.

The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.

How would this affect your answer to part (a) ?

Li bought a house at the start of 2016. Li assumes the value of the house, £ V, can be predicted using the formula

V = 185000 × 1.035ⁿ

where n is the number of years after the start of 2016.

Explain how you know that the value of the house is predicted to increase each year.

Write down the percentage increase per year that is used in the formula.

Write down the value of the house at the start of 2016.

Calculate the predicted value of the house at the start of 2020, giving your answer correct to 4 significant figures.

Compared with its value at the start of 2016, show that the formula predicts the house

will have doubled in value at some point during 2036.

Give one reason why this may not happen.

A car accelerates at 4.06 m/s² for 10.1 seconds from an initial velocity of 2.93 m/s.

Harper rounds each value to 1 significant figure. Harper uses the rounded values and the formula

to estimate the distance travelled in the 10.1 seconds. Harper’s answer is 430 metres.

Using Harper’s method, show that their answer is wrong.

Rearrange this formula to make t the subject.

Round 564 to the nearest ten.

Round 438 749 to 3 significant figures.

Charlie invests £9000 at a rate of 0.7% per year compound interest.

Calculate the total amount of interest Charlie will have earned after 5 years. Give your answer correct to the nearest penny.

Frankie and Taylor travel the same distance from town A to town B.

Frankie travels at an average speed of 52 kilometres per hour (km/h). Taylor travels at an average speed of 15 metres per second (m/s).

The journey takes Frankie 4 hours.

Calculate how long the journey takes Taylor. Give your answer in hours and minutes, correct to the nearest minute. You must show your working.

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 =

This table shows the names and areas of five lakes.

Write the area of Lake Mweru as an ordinary number.

Write the lakes in the order of their area, starting with the smallest.

smallest largest

Calculate the difference between the areas of Lake Ladoga and Lake Tana. Give your answer in standard form, correct to 2 significant figures.

Calculate.

(6² + 5)³

Write your answer correct to 3 significant figures.

This table shows the names and areas of five lakes.

Write the area of Lake Mweru as an ordinary number.

Write the lakes in the order of their area, starting with the smallest.

smallest largest

Calculate the difference between the areas of Lake Ladoga and Lake Tana. Give your answer in standard form, correct to 2 significant figures.

The table below shows the number of barrels of oil produced per day by some countries.

Write the number of barrels of oil produced per day by Cameroon as an ordinary number.

How many more barrels of oil per day did China produce than the UK? Give your answer in standard form, correct to 3 significant figures.

Jamal says the USA produced approximately three times more barrels of oil than Japan.

Is he correct? Show how you decide.

Jamal is........ because........

The table below shows the area, in square kilometres (km²), of some countries.

Write the area of Sweden as an ordinary number.

Which of the above countries has the smallest area?

Alexis says

The area of Australia is approximately three times larger than the area of Luxembourg

Is she correct? Show how you decide.

Alexis is........ because........

Work out the total area of Russia and Australia. Give your answer in standard form, correct to 2 significant figures.

Round 32 629 to the nearest thousand.

Round 32 629 to 1 significant figure.

Round 356 to the nearest ten.

Round 356.052 to 1 decimal place.

Find the value of y in each of the following.

3 × 3 × 3 × 3 = 3^y

6³ × 6⁵ = 6^y

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

Joan makes cups of tea and coffee at a lunch club. Each cup requires 250 ml of boiling water. She has a kettle that boils up to 1.7 litres of water each time.

She boils 10 litres of water in an urn. She then uses the kettle to boil the rest of the water she needs.

Find the least number of times that Joan needs to boil the kettle to make 56 cups. Show how you decide.

A grain of salt weighs 6.48 × 10^-5kg on average. A packet contains 0.35 kg of salt.

Use this information to calculate the number of grains of salt in the packet.

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

The diagram shows a regular hexagon made from six equilateral triangles. Each side is 10 cm. The angle ACB is a right angle.

Show that AC = 8.66 cm, correct to 3 significant figures.

Show that the area of triangle ACB is 21.7 cm², correct to 3 significant figures.

Find the area of the hexagon, giving your answer to an appropriate degree of accuracy.

Calculate.

Give your answer correct to 3 significant figures.

Claudia invests £25 000 at a rate of 2% per year compound interest.

Calculate the total amount of interest she will have earned after 5 years. Give your answer correct to the nearest penny.

A grain of salt weighs 6.48 × 10^-5kg on average. A packet contains 0.35 kg of salt.

Use this information to calculate the number of grains of salt in the packet.

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

Round 81.469 to 1 decimal place.

Round 0.005 694 to 3 significant figures.

Work out.

8 ÷ 0.4

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

A newborn baby has an approximate mass of 3.5 kilograms.

A human cell has an approximate mass of 2.7 × 10^-11 grams.

Use these values to estimate the number of human cells in a newborn baby. Give your answer in standard form, correct to 2 significant figures.

Two cylinders, A and B, are mathematically similar.

Cylinder A has volume 2400 cm³ and height 12 cm. Cylinder B has volume 750 cm³.

Find the height of cylinder B. Give your answer correct to an appropriate degree of accuracy.

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

A circle has radius 6 cm.

Calculate its circumference. Give your answer in centimetres, correct to 1 decimal place.

The scale diagram below shows two cities, P and Q.

A plane departs from P at 09 47 and arrives at Q at 12 07.

Work out the average speed, in kilometres per hour, of the plane.

Give one reason why your answer may be inaccurate.

Write down.

3091 rounded to the nearest hundred

3% as a decimal

the cube root of 27

Complete the statement below using a number from this list.

- 2 0 - 6 6

Write the following numbers in order of size, smallest first.

0.4 0.5 0.06 0.444 0.46

smallest

Calculate.

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.

Here is the floor plan of a rectangular room.

Tim buys carpet tiles for this room.

Each tile is a square measuring 50 cm by 50 cm. The tiles are only sold in packs of ten. Each pack costs £20. Tim pays for fitting at a rate of £7.50 per square metre, with any fraction of a square metre rounded up.

Work out the total cost of the tiles and fitting.

Round 7874 to

the nearest hundred,

1 significant figure.

Find the value of x.

A company makes sweets. The sweets are put into packets.

Here are some facts.

Calculate the mean number of sweets in one packet.

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

State one assumption you have made in part (c)(i).

A company makes sweets. The sweets are put into packets.

Here are some facts.

Calculate the mean number of sweets in one packet.

Sweets are made on 288 days each year.

Calculate the number of sweets made each year. Give your answer in standard form.

The company has 152 machines making the sweets. Each machine operates for 15 hours each day.

Calculate the number of sweets made by one machine each hour. Give your answer as an ordinary number correct to the nearest 10.

State one assumption you have made in part (c)(i).

Use one of these symbols <, > or = to make each statement true.

17.6........ 17.06

Round 184 329 to the nearest hundred.

Work out 17% of 54. Give your answer correct to 1 decimal place.

320 people go on a coach trip. Each coach holds 53 people.

Gary says 6 coaches are needed.

Is Gary correct? You must show your working.

A farmer has a field that is in the shape of a trapezium. He measures the field so that he can work out the area. He puts his measurements on this diagram of the field.

The farmer has rounded his measurements to two significant figures.

Give a reason why he may have done this.

The field produces 6400 kilograms of wheat per hectare. One hectare is 10 000 m².

Work out how many kilograms of wheat the field produces.

Round 7.306 5 to 2 decimal places.

Round each number to 3 significant figures.

408 231

0.006 137 02

This table shows the populations of the four countries of the UK in 2012. All values are given correct to 3 significant figures.

Write the population of England as an ordinary number.

Work out the total population of Wales, Scotland and Northern Ireland. Give your answer in standard form.

The total population of the UK is predicted to reach 73.3 million in 2037.

Calculate the predicted percentage increase in the UK population from 2012 to 2037. Give your answer correct to 2 significant figures.