Standard Index Form

All about powers and 10 to the power of something.

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Adding and subtracting numbers in standard index f

Convert them into ordinary numbers, do the calculation, then change them back if you want the answer in standard form.

 

For example.

 

4.5 × 104 + 6.45 × 105

= 45,000 + 645,000

= 690,000

= 6.9 × 105

 



 


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Multiplying and dividing numbers in standard form

Here you can use the rules for multiplying and dividing powers. Remember these rules:

  • To multiply powers you add, eg, 105× 103= 108
  • To divide powers you subtract, eg, 105÷ 103= 102

For Example

Simplify (2 × 103) × (3 × 106)

How to do it

Multiply 2 by 3 and add the powers of 10:

(2 × 103) × (3 × 106) = 6 × 109

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Zero, negative and fractional powers

We can also find zero, negative and fractional powers. The rules below apply to these powers.

PowerAnswerExamples a0 1 40 = 11000 = 1370 = 1

Anything to the power 0 is equal to 1.

a-b

(http://www.bbc.co.uk/schools/gcsebitesize/maths/images/powersrootshirev3_1.gif)

(http://www.bbc.co.uk/schools/gcsebitesize/maths/images/ma_powers_table0.gif)

a1/2

(http://www.bbc.co.uk/schools/gcsebitesize/maths/images/powersrootshirev3_2.gif)

(http://www.bbc.co.uk/schools/gcsebitesize/maths/images/fracsdecpersrev2_3.png)

a1/3

(http://www.bbc.co.uk/schools/gcsebitesize/maths/images/powersrootshirev3_4.gif)

9 to the power of 1/3 = 3

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Comments

daviesg

Simple examples of rules of standard form and indices

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