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Rough Answers

An exercise on rounding values in a calculation to find an approximate estimate of the answer.

Rounding Level 1 Level 2 Level 3 Level 4 Bounds Exam-Style Description Help More ...

This is level 4: real life problems and puzzles. You will be awarded a trophy if you get at least 9 correct and you do this activity online.

Andrew drinks 1.9 litres of water each day for three years. By rounding the amount of water and the number of days to one significant figure find the approximate amount of water he drinks during the three years. [One year = 365 or 366 days]


\(l\) Correct Wrong

Bella estimates the number of pounds in 498 kilograms using the fact that \(1kg\) ≈ \(2.2lb\) and by rounding the numbers she uses in her calculation to one significan figure. What was the answer she got?


\(lb\) Correct Wrong

Chris makes a quick estimate of how many people weighing \(82kg\) will fit into a lift with a maximum load warning of \(920kg\). He does this by rounding the values used in the calculation to one significant figure. What was his answer?


Correct Wrong

Write down this calculation with each of the numbers rounded to one significant figure. Now work out the value of this new calculation.$$\frac{75.6 + 84}{9.31 - 72.9 ÷ 11.5}$$


Correct Wrong

Diana changed £715 to Fijian Dollars($) when the rate was £1 = $2.863. She first estimated the amount she would receive by rounding the two numbers she used in her calculation to one significant figure. How many dollars did she expect to receive?


$ Correct Wrong

What is the value of the next square number after \(3.55^2\)?


Correct Wrong

What is the value of the next cube number after \(1.18^3\)?


Correct Wrong

Calculate an estimate for the circumference of a circle with diameter 5.88cm by rounding the numbers used in your calculation to one significant figure.


cm Correct Wrong

The average amount of storage space needed for a photograph taken with Ed's phone is 3940 KB. The available storage space on Ed's laptop is 217 GB. By rounding these numbers to one significant figure estimate the number of photographs that could be stored on Ed's laptop.


Correct Wrong

Write down this calculation with each of the numbers rounded to the nearest integer. Now work out the value of this new calculation giving your answer to the nearest integer.$$\sqrt{(5.1+19.5)(12.7-10.9)}$$


Correct Wrong

Write down this calculation with each of the numbers rounded to one significant figure. Now work out the value of this new calculation.$$\frac{0.000866 \times 6200}{\sqrt{9790 \div 99.4}}$$


Correct Wrong

It is said that in an average lifetime of 79 years, each human is likely to swallow about 9 spiders while sleeping. Supposing that the population of the UK is around 67 million, estimate of the number of spiders consumed in this way in the UK each year? Give your answer correct to one significant figure.


Correct Wrong

This is Rough Answers level 4. You can also try:
Level 1 Level 2 Level 3


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Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

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When planning to use technology in your lesson always have a plan B!

Jen, Australia

Saturday, June 1, 2019

"I just tried level one. It looks like a great way to reinforce significant figures to students, through mental estimates! However, the question says give answers to one significant figure - and I just got most of the questions "wrong", as your answers are mostly to 2 significant figures."


Sunday, June 2, 2019

"Thanks very much for your feedback Jen. The instructions ask for the numbers in the questions to be rounded to one significant figure; not the answers. The answers should be given exact after the pre-calculation rounding has taken place. Once again thanks for the feedback, much appreciated."

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Description of Levels



Rounding - Before doing these exercises you will need to know how to round numbers to one significant figure.

Level 1 - Round the numbers in a basic calculation to one significant figure to obtain an approximate answer

Level 2 - Round the numbers to one significant figure to obtain an approximate answer to calculations including decimals and fractions

Level 3 - Determine whether an approximation is a over-estimate or an under-estimate if each of the numbers are rounded to one significant figure

Level 4 - Real life problems and puzzles

Bounds - Determine the upper and lower bounds when rounding or truncating quantities used in calculations.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Breathe Easily - A real-life question that can be (roughly) answered by making some approximations.

Fermi Problem - Unleash your approximating skills to estimate something quite unknown in this Advanced Starter.

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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