Unit conversion- Source: proprofs.com

## Unit conversion –

One unit can be converted into another by conversion factor method or dimensional analysis. In this method, multiply the given value by the conversion factor, retaining the units of the physical quantity & that of the conversion factor in such a way that all units cancel out leaving the required one.

Ex-  convert 13.5 m into cm,

1m = 100 cm

1= 100 cm / 1 m

100 cm / 1 m is called conversion factor

13.5 m = 13.5 m x 100 cm / 1 m = 1350 cm

## Relation between units-

### Length-

#### SI unit: Meter (m)

1 kilometer     = 1000 meter = 0.62137 mile
1 meter            = 100 centimeter
1 centimeter   = 10 millimeter
1 nanometer   = 1.00 x 10-9 meter
1 picometer    = 1.00 x 10-12 meter

1 Ångstrom   = 1.00 x 10-10 meter

1 mile= 1760 yard

1 yard =3 feet

1 feet = 12 inch

1 inch = 2.54 centimeter

1 mile= 1.609 kilometer = 5280 feet

### Volume-

#### SI unit: Cubic meter (m3)

1 liter (L) = 1 x 10-3m3 = 1000 ml or cm3 =  1 dm3  = 1.0567 quarts
1 gallon = 4.00 quarts

1 feet3  = 28.32 Liter

1 gallon  = 3.78541 litre

### Mass-

#### SI unit: Kilogram (kg)

1 kilogram = 1000 grams
1 gram   = 10 decigram= 100 centigram    = 1000 milligrams
1 pound     = 453.59237 gram = 16 ounces

1 ounce = 28.32 gram

1 ton = 1000 Kilogram

1 ton           = 2000 pounds

### Pressure-

#### SI unit: Pascal (Pa)

1 pascal = 1 N/m2 = 1 kg/m . s2
1 atmosphere = 101.325 kilopascal = 101325 pascal =760 mmHg = 760 torr = 1.013 x 10 6   dyne/cm2
1 atmosphere  = 14.70 lb/in2 = 1.01325 bar
1 bar = 105 Pa

## Other units-

1 dyne= 10-5 Newton

1 calorie = 4.184 Joule

1 erg = 10-5  Joule

1 electron volt = 1.6 x  10-19  Joule

## Some solved examples of Unit conversion-

Question 1- Convert each of the following in SI unit-

a) 0.25  Å

SI unit of distance is meter.

1 Ångstrom   = 10-10 meter

unit factor = 10-10 meter / 1 Å

0.25 Å= 0.25 Å x 10-10 meter / 1 Å = 0.25 x 10-10 meter

0.25 Å = 2.5 x 10-11 meter

b) 25 million mile

SI unit of distance is meter.

1 mile= 1.609 kilometer 1.609 x 1000 meter

unit factor = 1.609 x 1000 meter/ 1 mile

25 million mile = 25 x 10 6 mile  x 1.609 x 1000 meter/ 1 mile

25 million mile = 4.0225 x 1010 meter

c) density  = 0.234 gm / ml or gm /cm3

The SI unit of density is kg/m3

1 Kg = 1000 gm

1m= 100 cm

unit factor = 1 Kg/ 1000gm  & 100 cm / 1m

0.234 gm /cm3= 0.234 gm /cm3 x (1 Kg/ 1000gm) x (100 cm / 1m) 3

density = 0.234  gm /cm3 = 2340 kg/m3

Question 2 –  convert mass of electron i-e  9.1 x 10-28 gm into Kg

1 gm = 10-3  Kg

unit factor = 10-3  Kg / 1gm

9.1 x 10-28 gm = 9.1 x 10-28 gm x 10-3  Kg / 1gm

9.1 x 10-28 gm = 9.1 x 10-31 Kg