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Write Small Numbers in Standard Form

In this worksheet, students read and write small numbers in standard index form.

'Write Small Numbers in Standard Form' worksheet

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Interpret/Compare Standard Form Numbers

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Standard (index) form is a shorthand way of writing a very large or a very small number.

It is written as a  number between 1 and 10 (but not equal to 10) multiplied by a power of 10, for example 2.94 × 102 or 4.8 × 10-3.

In this worksheet, we will just look at very small numbers.

 

Example

Change 0.00000583 into standard form.

First fix the decimal point after the first non-zero digit, i.e. 5.83


Next determine the power of 10 that you must multiply 5.83 by, to get back to 0.00000583.  

In this case it is -6.

In other words, we divide 5.83 by 10 six times to get to 0.00000583.


So 0.00000583 = 5.83 × 10-6

 

Other Examples


0.0000001122 = 1.122 × 10-7

0.00000006 = 6 x 10-8

Change the following number to one written in standard form:

0.0000513

5.13 x 10-5

5.13 x 10-6

5.13 x 10

Change the following number to one written in standard form:

0.000623

6.23 x 10-5

6.23 x 10-4

623 x 10-4

Change the following number to one written in standard form:

0.0006

6 x 104

6 x 10-4

6 x 10-3

Change the following number to one written in standard form:

0.00000604

6.04 x 10-6

60.4 x 10-5

6.04 x 10-5

Change the following number to one written in standard form:

0.0000001234

1234 x 10-4

1.234 x 10-7

0.1234 x 10-8

Change the following number to one written in standard form:

0.1008

1.008 x 101

1.008 x 0.1

1.008 x 10-1

Change the following number to one written in standard form:

0.004

4 x 10-3

4-3

4 x 10-2

Change the following number to one written in standard form:

0.00002

0.2 x 10-5

2 x 10-3

2 x 10-5

Change the following number to one written in standard form:

0.000000000020002

2.0002 x 10-11

2 x 10-11

2.2 x 10-11

Change the following number to one written in standard form:

0.0000000009

9 x 10-9

9 x 109

9 x 10-10

  • Question 1

Change the following number to one written in standard form:

0.0000513

CORRECT ANSWER
5.13 x 10-5
EDDIE SAYS
For a x 10b a must be between 1 and 10 (.13) To get from 5.13 to 0.0000513 we divide by 10 five times
  • Question 2

Change the following number to one written in standard form:

0.000623

CORRECT ANSWER
6.23 x 10-4
EDDIE SAYS
For a x 10b a must be between 1 and 10 (6.23) To get from 6.23 to 0.000623 we divide by 10 four times
  • Question 3

Change the following number to one written in standard form:

0.0006

CORRECT ANSWER
6 x 10-4
EDDIE SAYS
For a x 10b a must be between 1 and 10 (6) To get from 6 to 0.0006 we divide by 10 four times
  • Question 4

Change the following number to one written in standard form:

0.00000604

CORRECT ANSWER
6.04 x 10-6
EDDIE SAYS
For a x 10b a must be between 1 and 10 (6.04) To get from 6.04 to 0.00000604 we divide by 10 six times
  • Question 5

Change the following number to one written in standard form:

0.0000001234

CORRECT ANSWER
1.234 x 10-7
EDDIE SAYS
For a x 10b a must be between 1 and 10 (1.234) To get from 1.234 to 0.0000001234 we divide by 10 seven times
  • Question 6

Change the following number to one written in standard form:

0.1008

CORRECT ANSWER
1.008 x 10-1
EDDIE SAYS
For a x 10b a must be between 1 and 10 (1.008) To get from 1.008 to 0.1008 we divide by 10 once.
  • Question 7

Change the following number to one written in standard form:

0.004

CORRECT ANSWER
4 x 10-3
EDDIE SAYS
For a x 10b a must be between 1 and 10 (4) To get from 4 to 0.004 we divide by 10 three times
  • Question 8

Change the following number to one written in standard form:

0.00002

CORRECT ANSWER
2 x 10-5
EDDIE SAYS
For a x 10b a must be between 1 and 10 (2) To get from 2 to 0.00002 we divide by 10 five times
  • Question 9

Change the following number to one written in standard form:

0.000000000020002

CORRECT ANSWER
2.0002 x 10-11
EDDIE SAYS
For a x 10b a must be between 1 and 10 (2.0002) To get from 2.0002 to 0.000000000020002 we divide by 10 eleven times
  • Question 10

Change the following number to one written in standard form:

0.0000000009

CORRECT ANSWER
9 x 10-10
EDDIE SAYS
For a x 10b a must be between 1 and 10 (9) To get from 9 to 0.0000000009 we divide by 10 nine times
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