# Powers And Roots

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## Maths- Standard Form

Standard index form is also known as standard form. It is very useful when writing very big or very small numbers.

In standard form, a number is always written as: A × 10 n

A is always between 1 and 10. n tells us how many places to move the decimal point.

Example : Write 15 000 000 in standard index form.

Solution

15 000 000 = 1.5 × 10 000 000

This can be rewritten as:

1.5 × 10 × 10 × 10 × 10 × 10 × 10 × 10

= 1. 5 × 10 7

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## Standard Form 2

You can convert from standard form to ordinary numbers, and back again. Have a look at these examples:

3 x 104 = 3 × 10 000 = 30 000 (Since 104 = 10 × 10 × 10 × 10 = 10 000)

2 850 000 = 2.85 × 1 000 000 = 2.85 × 106 Make the first number between 1 and 10.

0.000467 = 4.67 × 0.0001 = 4.67 × 10 -4

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## Adding And Subtracting Numbers In Standard Form

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

Example 1

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

Example 2

Simplify (2 × 103) × (3 × 106)

Solution

Multiply 2 by 3 and add the powers of 10:

(2 × 103) × (3 × 106) = 6 × 109

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