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# Standard Form And Approximation

STANDARD FORM: Is a convenient way of writing very large or small numbers.  It is the product of the numbers in powers of 10 to determine the position of the decimal point and it´s writing between 1 and 9 i.e.  a X . Where a is the number between 1and 9 and n is the position of the decimal point.

### EXAMPLE:

Express the following numbers in standard form;

• 9 (b) 54.6  (c) 570200

SOLUTION.

• 9 = 9 x 100 (b)  6 = 5.46 x 101  (c) 570200 = 5.702 x 105

## NEGATIVE POWERS (NUMBERS LESS THAN 1)

Express the following numbers in standard form;

• 02 (b) 0.000175

SOLUTION

• 02 = 2 x 10-2 (b) o.000175 =1.75 x 10-4

# MULTIPLICATION AND DIVISION OF STANDARD FORM

Simplify the following:

• 222 x 10-4 x 6.32 x 104 (b)  2.8 x 108  ÷ 1.5 x 104

SOLUTION

• (8.222 x 6.32) x (10-4 x 104)) = 51.96304 x 10-4+4

5.196304 x 10x100  = 5.196304 x 101

(b) (2.8  1.5) x ( 10÷ 104) = 1.86667 x 108-4

#### 1.86667 x 104

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