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

##### RoundingLevel 1Level 2Level 3Level 4BoundsExam-StyleDescriptionHelpMore ...

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 an 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] Working: $$l$$ Bella estimates the number of pounds in 692 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? Working: $$lb$$ Chris makes a quick estimate of how many people weighing $$82kg$$ will fit into a lift with a maximum load warning of $$910kg$$. He does this by rounding the values used in the calculation to one significant figure. What was his answer? Working: Write down this calculation with each of the numbers rounded to one significant figure. Now work out the value of this new calculation.$$\frac{86.6 + 44}{3.37 - 12.9 ÷ 11.5}$$ Working: Diana changed £815 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? Working: \$ What is the value of the next square number after $$7.55^2$$? Working: What is the value of the next cube number after $$8.18^3$$? Working: Calculate an estimate for the circumference of a circle with diameter 8.88cm by rounding the numbers used in your calculation to one significant figure. Working: cm 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. Working: 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.$$\sqrt{(6.1+18.6)(17.8-15.6)}$$ Working: Write down this calculation with each of the numbers rounded to one significant figure. Now work out the value of this new calculation.$$\frac{0.000354 \times 6100}{\sqrt{4830 \div 46.8}}$$ Working: 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. Working:
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This is Rough Answers level 4. You can also try:
Level 1 Level 2 Level 3

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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#### Remainder Race

A brilliant game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number. There are one and two player versions and the rules are inspired by the Royal Game of Ur.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Teachers

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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."

Transum,

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

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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.

## Example

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