Numbers - Standard Form, Scientific and Engineering 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 10⁶ 

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 10^x x N₂ 10^y = (N₁ x N₂) 10^{x + y}           (1)

Multiplcation Example

4.3 10⁴  x 2.4 10³  =

(4.3 x 2.4) 10⁴⁺³ =

10.32  10⁷

Division

N₁ 10^x / N₂ 10^y = (N₁ / N₂) 10^{x - y}           (2)

Division Example

4.3 10⁴  / 2.4 10³  =

(4.3 / 2.4) 10^4-3 =

1.79  10¹

Temperature ^oC
K
^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 kg_f
N
lbf

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

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm