Upper and Lower Bounds

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.

	You are learning this because future ideas are built on previous ideas and the more ideas you learn the more power you have to learn anything, ever! The world's best football player engages in rigorous training, practicing skills repeatedly to prepare for the big game. While the specific actions rehearsed during these exercises are rarely needed in the match, the very process of performing these drills enhances their overall prowess as a top player. more...	More Activities: Maths Map Go Maths Games Puzzles Times Tables TablesMaster iPad Maths Investigations Exam Questions
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 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)." Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"		Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity Maths Mind Reader This spectacular magic trick never fails to amaze people of all ages assuming they can add and subtract very simple numbers. The mathematics comes in finding out how the trick works.	Answers There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe
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. Maths Map Are 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.
Teachers
If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:	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.	It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B!
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program

Description of Levels

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 - Mixed calculations involving upper and lower bounds.

Level 6 - Upper and lower bounds of algebraic expressions.

Exam Style questions are in the style of GCSE or IB/A-level 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.

Extension

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.

1. The length of a pencil, p millimetres, is rounded to the nearest ten millimetres. The length is given as 150mm. What are the limits of accuracy?	≤ p <
2. A set of kitchen scales displays readings to the nearest ten grams. Find the upper and lower bounds in grams for a weight, w, displayed as 230g. 230g	g ≤ w < g
3. A digital thermometer measures temperatures (T) to the nearest two degrees. Find the range of possible temperatures if the display shows 78^o. 78^o	^o ≤ T < ^o
4. A number, D, is rounded to the nearest ten. The result is 440. What are the limits of accuracy?	≤ D <
5. The weight of a box of bolts (w) is rounded to the nearest 50g. If the weight of the box is given as 2500g What are the limits of accuracy.	g ≤ w < g
6. A number, F, is rounded to the nearest fifty. The result is 3250. What are the limits of accuracy?	≤ F <
7. The length of a fibre-optic cable (L) is rounded to the nearest fifty metres. If the length is given as 3600m find the range of values within which the actual length of the cable could be.	m ≤ L < m
8. A number, H, is rounded to the nearest twenty. The result is 1780. What are the limits of accuracy?	≤ H <
9. A plumbing supplier sells pipes cut to size. The length (L millimetres) of the cut pipe is rounded to the nearest twenty millimetres in order to calculate the cost. If the length of a particular piece of pipe is given as 1840 find the range of values within which the actual length could be.	≤ L <
10. A number, J, is rounded to the nearest one hundred. The result is 10100. What are the limits of accuracy?	≤ J <

Upper and Lower Bounds

Determine the upper and lower bounds when rounding quantities used in calculations.

Menu Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Exam Help More

Instructions

More Activities:

Featured Activity

Maths Mind Reader

Answers

Go Maths

Maths Map

Teachers

Description of Levels

Extension

Help Video