Rounding to a given power of ten

Practise your approximation and rounding skills with this online, self-marking exercise.

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This is level 7; Rounding numbers to the nearest ten, hundred etc. You can earn a trophy if you get at least 9 correct.

 7124[to the nearest ten] 1960.8[to the nearest ten] 9890.1[to the nearest ten] 5261[to the nearest hundred] 5377.2[to the nearest hundred] 9990.2[to the nearest hundred] 9876[to the nearest thousand] 525[to the nearest thousand] 86[to the nearest thousand] 42259[to the nearest ten thousand] 6528260[to the nearest hundred thousand] 2841264[to the nearest million]
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This is 'Rounding to a given power of ten'. You can also try rounding to:
Whole number 1 decimal place 2 decimal places 1 sig fig 2 sig figs 3 sig figs

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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Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

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"This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register."

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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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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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When planning to use technology in your lesson always have a plan B!

QI,

Monday, February 28, 2022

"Who was the first person to put two feet on the top of Everest?

It was Radhanath Sikdar who had a special aptitude for trigonometry. Back in the 1850s he used a theodolite located 150 miles away to measure the height as being exactly 29,000 feet. He thought people would not be impressed with the accuracy of his measurement as it was a multiple of a thousand so he added two feet to make the measurement 29,002 feet. Thus he became the first person to put two feet on the top of Everest!
Quite Interesting!"

Lauri Johnson, Eastern Hancock High School

Monday, August 14, 2023

"Some of the questions for 3 sigfigs require the student to write the answer so that it only has 2 sigfigs. For example, 87954 to 3 sigfigs is 8.80 x 10^4, but the practice wants the answer to be 88000. But that answer only has 2 sigfigs. Only a few questions come up like this, but I wanted to pass is along. Other than that, this is a GREAT practice for my chem students. Thanks for making this available.

[Transum: Thanks very much Lauri, that's an excellent point. I have added information to the Help tab to explain the situation with examples of how to avoid ambiguity.]"

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.

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Description of Levels

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Level 1 - Rounding numbers to the nearest whole number

Level 2 - Rounding numbers to one decimal place

Level 3 - Rounding numbers to two decimal places

Level 4 - Rounding numbers to one significant figure

Level 5 - Rounding numbers to two significant figures

Level 6 - Rounding numbers to three significant figures

Level 7 - Rounding numbers to the nearest ten, hundred etc

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Example

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. You can double-click the 'Check' button to make it float at the bottom of your screen.

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.

Ways to denote significant figures in an integer with trailing zeros

Adapted from a longer piece in a Wikipedia article

The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if the number 1300 is precise to the nearest unit (just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundreds due to rounding or uncertainty. The following widely recognised options are available for indicating the significance of number with trailing zeros:

• Eliminate ambiguous or non-significant zeros by changing the unit prefix in a number with a unit of measurement. For example, the precision of measurement specified as 1300 g is ambiguous, while if stated as 1.30 kg it is not.
• Eliminate ambiguous or non-significant zeros by using Scientific Notation: For example, 1300 with three significant figures becomes 1.30×103.
• Explicitly state the number of significant figures (the abbreviation s.f. is sometimes used): For example "20 000 to 2 s.f." or "20 000 (2 sf)".
• State the expected variability (precision) explicitly with a plus–minus sign, as in 20 000 ± 1%. This also allows specifying a range of precision in-between powers of ten.

For the purpose of answering the questions in the higher level exercises these methods are not necessary as your typed answers appear on the same page as the instructions stating the number of significant figures required.

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