Rounding, Estimation & Error Intervals Practice Questions

Write $6.0472$ correct to 2 decimal places.

Write $34\,682$ correct to the nearest $1000$.

Write $0.007\,391$ correct to 2 significant figures.

Write down an estimate for the real height, in metres, of the woman.

....................... metres

Write down an estimate for the real height, in metres, of the lamp post.

....................... metres

Write down the least possible mass of the lorry.

....................... kg

Write down the greatest possible mass of the lorry.

....................... kg

Work out an estimate for the value of $7.4 \times 23.8$

You must show your working.

Is your answer to part (a) an underestimate or an overestimate?

Give a reason for your answer.

Ryan works out $\dfrac{31.4 \times 9.7}{0.48}$

He says the answer is $63.45$

Use approximations to show that Ryan is wrong.

You must show your working.

The mass, $m$ kg, of a parcel is $3.8\text{ kg}$ correct to 1 decimal place.

Write down the error interval for $m$.

A jug contains $c$ litres of water.

The volume of water is $2.4$ litres truncated to 1 decimal place.

Write down the error interval for $c$.

By rounding each number to 1 significant figure, work out an estimate for the cost of the turf for the lawn.

You must show your working.

Will the actual cost of the turf be more than or less than your estimate?

Give a reason for your answer.

A jar of coffee has a mass of $750\text{ g}$.

The jar of coffee costs $£4.99$.

Work out the cost of $100\text{ g}$ of this coffee.

Give your answer to an appropriate degree of accuracy.

Work out an estimate for the average speed of the train, in miles per hour.

You must show your working.

Is your answer to part (a) an underestimate or an overestimate of the average speed?

Give a reason for your answer.

Nadia is going to cover a garden path with gravel.

The path is a rectangle of length $28.6\text{ m}$ and width $1.9\text{ m}$.

Gravel is sold in bags.

Each bag of gravel covers $0.48\text{ m}^2$ of path.

Each bag of gravel costs $£3.95$.

Work out an estimate for the total cost of the gravel Nadia needs.

You must show your working.

A school is making $400$ gift bags for a charity event.

Each gift bag contains

• one pen costing $£0.78$
• one notebook costing $£1.87$
• one water bottle costing $£3.60$

The school has a budget of $£2800$ for the gift bags.

By rounding each cost to 1 significant figure, show that the school has enough money in its budget.

You must show your working and give a reason for your answer.