# 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 ^{4-3 }*

*=*

*1.79 10^{1}^{ }*