Rounding, Estimation & Bounds Practice Questions

Write $0.0068453$ correct to 2 significant figures.

Write $23\,961$ correct to 3 significant figures.

Write $7.0952$ correct to 2 decimal places.

The length has been rounded correct to 1 decimal place.

Using inequalities, write down the error interval for the length, $L$ metres.

In fact the length has been truncated to 1 decimal place.

Using inequalities, write down the error interval for the length, $L$ metres.

Write down the lower bound of the mass of the horse.

Write down the upper bound of the mass of the horse.

The height of the horse is $1.62$ m, correct to the nearest centimetre.

Using inequalities, write down the error interval for the height, $h$ metres.

Work out an estimate for the value of
$$\frac{28.7 \times 9.72}{\sqrt{0.0417}}$$
You must show your working.

A metal rod has length $1.8$ m, correct to the nearest $0.1$ m.

Gemma cuts a piece of length $47$ cm, correct to the nearest centimetre, from the rod.

Work out the upper bound of the length of the piece of rod that is left.
Give your answer in centimetres.

A number, $y$, is rounded to 1 significant figure. The result is $800$.

Using inequalities, write down the error interval for $y$.

The number of people at a concert was $4500$, correct to 2 significant figures.

Write down the least possible number of people at the concert.

Arun measures the mass and the volume of a block of metal.

Measurement	Value	Accuracy
Mass	$780$ g	correct to the nearest $10$ g
Volume	$96$ cm$^3$	correct to the nearest cm$^3$

Arun uses $\text{density} = \dfrac{\text{mass}}{\text{volume}}$.

Work out the upper bound for the density of the metal.
Give your answer correct to 3 significant figures.

A sphere has radius $5.2$ cm.

The surface area, $A$, of a sphere of radius $r$ is given by $A = 4\pi r^2$.

Work out an estimate for the surface area of the sphere.

Is your estimate an over-estimate or an under-estimate of the true surface area?
Give a reason for your answer.

Explain why the length has not been written to an appropriate degree of accuracy, and write down a more appropriate value for the length.

Turf costs $£4.29$ per square metre.

Work out an estimate for the cost of enough turf to cover the lawn.

The population density of a town, in people per square kilometre, is given by
$$\text{population density} = \frac{\text{population}}{\text{area}}$$
The population of Hartbury is $84\,000$, correct to 2 significant figures.
The area of Hartbury is $27$ km$^2$, correct to the nearest square kilometre.

Ali says, 'The population density of Hartbury is more than $3200$ people per km$^2$.'

Could Ali be right?
You must show how you get your answer.

A rectangle has length $12.6$ cm and width $7.4$ cm.
Each measurement is correct to 1 decimal place.

Work out the upper bound and the lower bound for the area of the rectangle.

Use your answers to part (a) to write down the area of the rectangle to a suitable degree of accuracy.
You must give a reason for your answer.

Zara says, 'My average speed was more than $21$ km/h.'

Could Zara be right?
You must show how you get your answer.

In fact the distance was measured correct to the nearest $0.5$ km.

Explain how this could affect your answer to part (a).