# Upper and Lower Bounds

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

##### Level 1Level 2Level 3Level 4Level 5Exam-StyleDescriptionHelpMore Rounding

This is level 2: quantities rounded to a given multiple. You can earn a trophy if you get at least 7 questions correct.

 1. The length of a pencil, p millimetres, is rounded to the nearest ten millimetres. The length is given as 110mm. 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 250g.250g ≤ w < 3. A digital thermometer measures temperatures (T) to the nearest two degrees. Find the range of possible temperatures if the display shows 72o.72o ≤ T < 4. A number, D, is rounded to the nearest ten. The result is 450. What are the limits of accuracy? ≤ D < 5. The numbers of pins in a box (n) is rounded to the nearest fifty. If the number of pins is given as 2950 find the smallest and largest number of pins that could be in the box. ≤ n < 6. A number, F, is rounded to the nearest fifty. The result is 3050. What are the limits of accuracy? ≤ F < 7. The numbers of supporters at a football match (S) is rounded to the nearest fifty. If the number of supporters is given as 3750 find the range of values within which the actual number of supporters could be. ≤ S < 8. A number, H, is rounded to the nearest twenty. The result is 1660. 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 1860 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 <
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This is Upper and Lower Bounds level 2. You can also try:
Level 1 Level 3 Level 4 Level 5

## 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

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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#### Playing Card Maths

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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.

## Maths Map

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## 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:

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## Description of Levels

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Level 1 - Numbers truncated to a given multiple.

Level 2 - Quantities rounded to a given multiple.

Level 3 - Numbers rounded to a number of decimal places.

Level 4 - 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/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.

## Examples

This video is from the excellent Corbettmaths.

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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