Unit Conversions

 

To convert any measurement from one unit to another you need to multiply it by a conversion factor.  A conversion factor will always be equal to one.  Whenever you multiply a measurement by one it does not change the value of the measurement only the units associated with the measurement.  The reason that a conversion factor is equal to one is that it is based upon the equivalency between the two units.  Each equivalency will generate two conversion factors, e.g. if the equivalency is:

 

 

then we can divide both sides of this equation by either 1000 mg or 1g, e.g.:

 

 

or:

 

 

and thereby generate the two conversion factors for this equivalency.

Now we can use these conversion factors to change a measurement from one unit to another.  Suppose we have weighed an object and found it to have a mass of 0.67 g.  We want to convert this mass into mg.  What follows is a step by step procedure:

1.                  First write down the starting value:

 

 

2.         Next we write a multiplication sign and a line for our future fraction:

 

 

3.         Next we place the units that we are converting from in the denominator and the units that we are converting to in the numerator of the fraction that will be our conversion factor:

 

 

4.         Next, we need to supply the appropriate value to the conversion factor.  From the two factors that we made above we insert the appropriate value, in this case "1000" goes into the numerator from the second conversion factor that we created based upon the equivalency of 1000 mg = 1g.:

 

 

5.         What remains now is to do the arithmetic, either using a calculator or doing it by hand on a piece of paper:

 

 

This procedure can also be used in multiple steps to make more difficult conversions.  Work the following problems to get comfortable with this method.

 

1.         10.3 g  =  ? mg

2.         13 mm  =  ? mm

3.         0.0067 g  =  ? mg

4.         30 cm  =  ? in  (1 in  =  2.54 cm)

5.         14 Km  =  ? m

6.         12 mi  =  ? Km  (1 Km  =  0.6

7.         6 ft  =  ? cm

8.         8,400 mg  =  ? oz (1 oz = 28 g)

9.         1 cup  =  ? mL  (2 cups = 1 pt & 2 pts = 1 qt)

10.       3 pts  =  ? L (1.06 qt = 1 L)

11.       12 gal  =  ? L

12.       2.3 Kg  =  ? mg

13.       45,693 mm  =  ? m

14.       1 m  =  ? in

15.       14 troy oz  =  ? Kg  (12 troy oz  =  1 lb)

16.       2.3 tons  =  ?  Kg  (1 ton = 2000 lbs;  1 Kg = 2.2 lbs)

17.       1.6 mm  =  ?  nm

18.       5.67 x 1013 nm = ? m

19.       0.0083 in  =  ? nm

20.       100 yds  =  ? mm

 

 

 

Giga-

G

1,000,000,000

109

Mega-

M

1,000,000

106

Kilo-

K

1,000

103

centi-

c

0.01

10-2

milli-

m

0.001

10-3

micro-

μ

0.000001

10-6

nano-

n

0.000000001

10-9