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 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 150. 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 < 2. A number, B, if not a multiple of fifty, is rounded up to the next multiple of fifty. The result is 300. What are the limits of accuracy? < B ≤ 3. 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 ≤ 4. A number, D, is truncated to a multiple of ten. The result is 480. What are the limits of accuracy? ≤ D < 5. A number, E, is truncated to a multiple of five. The result is 565. What are the limits of accuracy? ≤ E < 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 620 what is the shortest and longest the time could have actually been? ≤ m < 7. A number, G, if not already a multiple of five is rounded up to the next multiple of five. The result is 705. What are the limits of accuracy? < G ≤ 8. A number, H, is truncated to a multiple of twenty. The result is 840. What are the limits of accuracy? ≤ H < 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 ≤ 10. A number, J, is truncated to a multiple of fifty. The result is 1000. What are the limits of accuracy? ≤ J <
Check

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.

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.

More Activities:

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 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Car Park Puzzle

Can you get your car out of the very crowded car park by moving other cars forwards or backwards? There are five levels of increasing difficulty and the interactive interface makes this a fun problem solving exercise.

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.

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:

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 All:

Description of Levels

Close

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.

Close