# Standard Form 9

## Test your understanding of standard form (scientific notation) with this self-marking, multiple-choice quiz.

##### Menu Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9ExamHelp

You can earn a trophy if you get at least 7 questions correct.

1. Which of the following numbers is the largest?

 A. 3.4 x 103   B. 9.93 x 102   C. 9.6 x 105   D. 4.1 x 104   E. 6.93 x 104

2. Which of the following numbers is the smallest?

 A. 1.56 x 106   B. 7.69 x 106   C. 8.67 x 106   D. 9.26 x 106   E. 1.74 x 107

3. Which of the following numbers is the largest?

 A. 8.16 x 10-1   B. 7.61 x 10-5   C. 2.27 x 10-5   D. 8.73 x 10-3   E. 1.99 x 10-3

4. Which of the following numbers is the smallest?

 A. 1.52 x 10-3   B. 1.76 x 10-1   C. 3.8 x 10-3   D. 7.55 x 10-6   E. 4.28 x 10-6

5. Evaluate (5.2 x 102)2

 A. 5.2 x 104   B. 27.04 x 104   C. 2.704 x 103   D. 2.704 x 105   E. 5.2 x 104

6. Evaluate (7.5 x 10-2)3

 A. 7.5 x 10-8   B. 421.875 x 10-8   C. 4.21875 x 100   D. 4.21875 x 10-4   E. 7.5 x 10-6

7. If a = 9.4 x 100, b = 5.6 x 10-1 and c = 7.5 x 10-4, what is ab÷c to two decimal places?

 A. 394,800.00   B. 223.81   C. 7,018.67   D. 66,270.00   E. 394,800.00

8. If a = 6.9 x 100, b = 6.5 x 101 and c = 9.4 x 10-2, what is a + b − c to two decimal places?

 A. 71.81   B. 71.99   C. -58.19   D. -58.01   E. 72

9. The dimensions of a water tank in the shape of a cuboid are 9 x 103mm,
5.6 x 103mm and 5.2 x 103mm. What is the capacity of the tank in standard form to 2 decimal places?

 A. 2.62 x 109 m3   B. 2.62 x 102 m3   C. 2.62 x 1027 m3   D. 26.21 x 1010 m3   E. 2.62 x 104 m3

10. The speed of light is approximately 3 x 108 metres per second. Express this in kilometres per hour in standard form to 3 significant figures.

 A. 1.08 x 109   B. 3.00 x 105   C. 1.08 x 1012   D. 3.00 x 109   E. 108 x 107

This is Standard Form 9 level 9. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8

## Instructions

Try your best to answer the questions above. Choose one of the five possible answers. When you have finished click the "check" button. If you have any questions wrong, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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## Description of Levels

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Level 1 - Converting from standard form. Positive indices.

Level 2 - Converting from standard form. Negative indices.

Level 3 - Converting from standard form. Mixed including zero as the index.

Level 4 - Converting to standard form. The inverse of level 1.

Level 5 - Converting to standard form. The inverse of level 2.

Level 6 - Converting to standard form. The inverse of level 3.

Level 7 - Mixed calculations.

Level 8 - Mixed calculations without a calculator.

Level 9 - Multiple choice exercise.

Standard Form Algebra - Deeply test your understanding of standard form by involving a little algebra.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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## Curriculum Reference

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

## Standard Form

Standard form, also known as scientific notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation.

## Examples

To convert a number to standard form means to write it in the form a x 10b where a is a number greater than or equal to one and less than ten and b is an integer.

34800

= 3.48 x 10000

= 3.48 x 10 x 10 x 10 x 10

= 3.48 x 104

0.0348

= 3.48 ÷ 100

= 3.48 x 1100

= 3.48 x 10-2

Finally note that any number raised to the power zero is 1 so:

3.48

= 3.48 x 1

= 3.48 x 100

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