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Numbers - Standard Form, Scientific and Engineering Notation

The difference between standard, scientific and engineering number notation.

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Standard Form or Scientific Notation

A number written with one digit to the left of the decimal point and multiplied by 10 raised to some power is written in standard form or with scientific notation, ex.

43712 = 4.3712 104  

0.036 = 3.6 10-2 

Engineering Notation

Engineering notation is similar to scientific notation except that the power of ten is always a multiple of 3, ex.

43712 = 43.712 103

          = 0.043712 10

0.036 = 36 10-3

         = 36000 10-6

Units used in engineering may be made smaller or larger with the use of prefixes, ex.

4.7 kJ = 4.7 103 J

         = 4700 J

8 MV = 8 106 V

       = 8000000 V

Prefixes used in the SI system.

Addition and Subtraction

Numbers written in scientific or engineering notation can be added or subtracted after they have been written with the same exponent. Example 

4.3 104 + 2.4 103  =

4.3 104 + 0.24 104 =

(4.3 + 0.24) 104 =

4.54  104

Multiplication and Division

Numbers written in scientific or engineering notation can be multiplied or divided with the rules of exponential numbers.


N1 10x x N2 10y = (N1 x N2) 10x + y           (1)

Multiplcation Example

4.3 10 x 2.4 103  =

(4.3 x 2.4) 104+3 =

10.32  107


N1 10x / N2 10y = (N1 / N2) 10x - y           (2)

Division Example

4.3 10 / 2.4 103  =

(4.3 / 2.4) 104-3 =

1.79  101

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