**Unit Cancellation Using the Metric System**

Sample problem: Convert 5.712 g into mg.

Solution:

a) write the number and unit given in the problem,

b) write a multiplication operator,

c) draw a horizontal line,

d) write an equal sign,

e) leave a space and then

f) write the unit to which you are converting.

The horizontal line represents the conversion factor we will use to change grams to milligrams.

To set up the conversion factor, take the unit from the measurement given in the problem (in this case g) and write it as the denominator of the conversion factor.

Write the unit to which you are converting (in this case mg) in the numerator of the conversion factor.

Determine which of the units in the converstion factor is larger and put the number one in front of it.

Determine the distance between the two prefixes in the conversion unit (in this case it is 3). Write this as a positive unit in front of the smaller prefix.

Grams will cancel out and the units mg will be on both sides of the equation i.e. the units will agree on both sides. Do the arithmetic and you have your answer 5.712 x 10^{3} mg.