Numbers  Standard Form, Scientific and Engineering Notation
The difference between standard, scientific and engineering number notation.
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 10^{4 }
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 10^{3}
= 0.043712 10^{6 }
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 10^{3} J
= 4700 J
8 MV = 8 10^{6} 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 10^{4 }+ 2.4 10^{3} =
4.3 10^{4 }+ 0.24 10^{4} =
(4.3 + 0.24) 10^{4} =
4.54 10^{4}^{ }
Multiplication and Division
Numbers written in scientific or engineering notation can be multiplied or divided with the rules of exponential numbers.
Muliplication
N_{1} 10^{x} x N_{2} 10^{y} = (N_{1} x N_{2}) 10^{x + y} (1)
Multiplcation Example
4.3 10^{4 } x 2.4 10^{3} =
(4.3 x 2.4) 10^{4+3 }=
10.32 10^{7}
Division
N_{1} 10^{x} / N_{2} 10^{y} = (N_{1} / N_{2}) 10^{x  y} (2)
Division Example
4.3 10^{4 } / 2.4 10^{3} =
(4.3 / 2.4) 10^{43 }=
1.79 10^{1}^{ }
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