ConversionsOften while solving problems it is necessary to change from one set of units to another. For example lengths may be given in miles and the answer requires that the lengths be metric, i.e. kilometers. It is then necessary to know how many kilometers there are in a mile: 1 mile = 1.609 kilometers If the original units were given in feet and the following are known: 1 mile = 1.609 kilometers 1 mile = 5280 feet Then two conversions are needed: from feet to miles and then from miles to kilometers.
To carry out conversions then two things are needed:
For example: If the distance between two buildings is 2000 feet, what is the distance in kilometers? Since 1 mile = 5280 feet 1 = 5280 feet/1 mile (the ratio 5280 feet/1 mile equals 1 was arrived at by dividing each side of the original conversion equation given above by 1 mile) 1 = 1 mile/5280 feet is also true (the ratio 1 mile/5280 feet equals 1 was arrived at by dividing each side of the original conversion equation by 5280 feet)
Also since 1 mile = 1.609 kilometers 1 = 1.609 kilometers/1 mile and 1 = 1 mile/1.609 kilometers To return to the problem: 2000 feet = ? kilometers. Convert feet to miles by choosing the conversion ratio that will eliminate the feet units: 1mile/5280 feet. This accomplishes the goal since the feet term in the denominator of the ratio cancels the feet term in the numerator of the original number. 2000 feet x 1mile/5280 feet = 2000/5280 miles = .379 miles Next convert miles to kilometers in the same way. Chose the conversion ratio that will eliminate the miles units (i.e. the ratio that has miles in the denominator) 1.609 kilomters/1 mile = 1 .379 miles x 1.609 kilomters/1 mile = .610 kilometers. Of course the two steps may be written in one equation: 2000 feet x 1mile/5280 feet x 1.609 kilomters/1 mile = .610 kilometers. The advantage of carrying out conversions in this way is that you can keep track of what you are doing and so you can be sure that you carried out the conversions correctly. Some useful conversion equations are given in the tables below. (Unsure of the abbreviations used below? Click here). If you do not find what you want or would like to try other conversions click here. 
LENGTH 


1 m 
100 cm 

1 mm 
1000 m 

1 m 
3.281 ft 

1 ft 
0.3048 m 

1 ft 
30.48 cm 
Can you calculate this from the information above? 
1 mi. 
1.609 km 

1 mi. 
5280 ft 

1 in 
2.54 cm 

1 ft 
12 in 

1 nm 
10^{9} m 

1 Å 
10^{10} m 
Angstrom unit 
1 AU 
1.5 x 10^{8} km 
Astronomical unit 
AREA 

1 ha 
100 m^{2} 
1 mi^{2} 
640 ac 
VOLUME 

1 L 
1000 cm^{3} 
1 L 
1000 mL 
1 mL 
1 cm^{3} 
1 ft^{3} 
7.481 gal 
MASS 


1000 g 
1 mg 
.0001 g 
1 oz 
.0352 g 
1 kg 
2.2 lb. 
1 lb. 
16 oz 
1 ton 
2000 lb. 
1 metric ton (= 1 tonne) 
1000 kg 