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# 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 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.

#### Muliplication

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

#### Division

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

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

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## Unit Converters

Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

9 1

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