# 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 4: quantities rounded to a number of significant figures. You can earn a trophy if you get at least 7 questions correct.

 1. The number of matches in a box, M, is given as 50. This number has been rounded to one significant figure. What is the least and most matches that could be in the box? ≤ M < 2. The number of trees in a forest, F, is given as 70. This number has been rounded to one significant figure. What is the least and most trees that could be in the forest? ≤ F < 3. The number of points scored in a game, P, is given as 700. This number has been rounded to one significant figure. What is the lowest and highest number of points that could have been scored? ≤ P < 4. A train's speed (v kph) is rounded to two significant figures. If the speed is given as 140 kph, what is the slowest and fastest it could have actually been travelling? ≤ v < 5. Another train's speed (w kph) is rounded to three significant figures. If the speed is also given as 140 kph, what is the slowest and fastest it could have actually been travelling? ≤ w < 6. The length of a curtain, L, is measured to be 1.22m to three significant figures. What is the shortest and longest the curtain could be? (give your answers in metres) ≤ L < 7. The length of a train, T, is listed as 64.0m to three significant figures. What, in metres, are the upper and lower bounds of the train's length? ≤ T < 8. The probability, p, of a certain event occuring has been calculated to be 0.0987 to three significant figures. What are the limits of accuracy? ≤ p < 9. The time taken (t seconds), for a particular insect to react to a sound was measured to be 0.800 seconds to three significant figures. What are the limits of accuracy? ≤ t < 10. A number, N, is 7.00 to three significant figures. What are the limits of accuracy? ≤ N <
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This is Upper and Lower Bounds level 4. You can also try:
Level 1 Level 2 Level 3 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.

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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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## 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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