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Upper and Lower Bounds

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

Level 1 Level 2 Level 3 Level 4 Level 5 Exam-Style Description Help More Rounding

This is level 1: numbers truncated to a given multiple. You can earn a trophy if you get at least 7 questions correct.

1. A number, A, if not a multiple of ten, is rounded down to the previous multiple of ten. The result is 110. What is the smallest the number could have been? What is the largest the number could have been? Type you answers into the boxes on the right to make the inequalities true. ≤ A < Correct Wrong
2. A number, B, if not a multiple of fifty, is rounded up to the next multiple of fifty. The result is 250. What are the limits of accuracy? < B ≤ Correct Wrong
3. Bus

Bluehound buses can hold ten passengers. To determine how many buses are needed for a large group the number of people in the group (if it is not already a multiple of ten) is rounded up to the next multiple of ten then this is divided by ten. If the number of buses booked for the factory workers' outing was 32, what is the smallest and largest number of people that could have been in the group?
< n Correct Wrong
4. A number, D, is truncated to a multiple of ten. The result is 490. What are the limits of accuracy? ≤ D < Correct Wrong
5. A number, E, is truncated to a multiple of five. The result is 500. What are the limits of accuracy? ≤ E < Correct Wrong
6. You can receive points in a game for the number of minutes, m, you keep the trolls at bay. The time is truncated to a multiple of five minutes. If a player's time is displayed as 655 what is the shortest and longest the time could have actually been? m < Correct Wrong
7. A number, G, if not already a multiple of five is rounded up to the next multiple of five. The result is 785. What are the limits of accuracy? < G ≤ Correct Wrong
8. A number, H, is truncated to a multiple of twenty. The result is 880. What are the limits of accuracy? ≤ H < Correct Wrong
9. A number, I, if not already a multiple of twenty is rounded up to the next multiple of twenty. The result is 940. What are the limits of accuracy? < I ≤ Correct Wrong
10. A number, J, is truncated to a multiple of fifty. The result is 1050. What are the limits of accuracy? ≤ J < Correct Wrong
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This is Upper and Lower Bounds level 1. You can also try:
Level 2 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.

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Practice Papers

Practice Papers

Mathematics GCSE(9-1) Higher style questions and worked solutions presented as twenty short, free, practice papers to print out.

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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.

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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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