Upper and Lower BoundsDetermine the upper and lower bounds when rounding quantities used in calculations. 
This is level 4: discrete and continuous quantities rounded to a number of significant figures. You can earn a trophy if you get at least 7 questions correct.
InstructionsTry 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. 



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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? Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc  in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is  my pupils love it! Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School: "This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register." 
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Go MathsLearning 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. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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Level 1  Numbers truncated or rounded up or down to a given multiple.
Level 2  Quantities rounded to the nearest multiple.
Level 3  Numbers rounded to a number of decimal places.
Level 4  Discrete and continuous quantities rounded to a number of significant figures.
Level 5  Calculations involving upper and lower bounds.
Exam Style questions are in the style of GCSE or IB/Alevel exam paper questions and worked solutions are available for Transum subscribers.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
Students who are also studying Physics may want to investigate a topic called Propagation of Uncertainties that uses these formulas.
$$ \text{If} \quad y= a \pm b \quad \text{then} \quad \Delta y = \Delta a + \Delta b $$ $$ \text{If} \quad y= \frac{ab}{c} \quad \text{then} \quad \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c} $$ $$ \text{If} \quad y= a^n \quad \text{then} \quad \frac{\Delta y}{y} = \begin{vmatrix} n \frac{\Delta a}{a} \end{vmatrix} $$The triangular symbols are the Greek letter delta and represent the errors or, more accurately, uncertainties.
Some of the questions in level 4 are about descrete quantities such as the number of matches in a matchbox. In this case it is not possible to have a fraction of a match, the number of matches must be an integer.
Example: The number of matches in a box, \(n\), is given as 80 to the nearest 10. The error bounds would be written as:
$$ 75 \le n \le 84 $$Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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