Mathematics: Units of Measurement

Metric Measurement Prefixes
Giga-: one billion (1 gigawatt is one billion watts)
Mega-: one million (1 megahertz is one million hertz)
Kilo-: one thousand (1 kilogram is one thousand grams)
Deci-: one tenth (1 decimeter is one tenth of a meter)
Centi-: one hundredth (1 centimeter is one hundredth of a meter)
Milli-: one thousandth (1 milliliter is one thousandth of a liter)
Micro-: one millionth (1 microgram is one millionth of a gram)

Measurement Conversion
When converting between units, the goal is to maintain the same meaning but change the way it is displayed. In order to go from a larger unit to a smaller unit, multiply the number of the known amount by the equivalent amount. When going from a smaller unit to a larger unit, divide the number of the known amount by the equivalent amount.
For complicated conversions, it may be helpful to set up conversion fractions. In these fractions, one fraction is the conversion factor. The other fraction has the unknown amount in the numerator. So, the known value is placed in the denominator. Sometimes the second fraction has the known value from the problem in the numerator, and the unknown in the denominator. Multiply the two fractions to get the converted measurement.

Note that since the numerator and the denominator of the factor are equivalent, the value of the fraction is 1. That is why we can say that the result in the new units is equal to the result in the old units even though they have different numbers.
It can often be necessary to chain known conversion factors together.

As an example, consider converting 512 square inches to square meters. We know that there are 2.54 centimeters in an inch and 100 centimeters in a meter, and that we will need to square each of these factors to achieve the conversion we are looking for.


Common Units and Equivalents




Volume and Weight Measurement Clarifications
Always be careful when using ounces and fluid ounces. They are not equivalent.






Having one pint of something does not mean you have one pound of it. In the same way, just because something weighs one pound does not mean that its volume is one pint.

In the United States, the word 'ton' by itself refers to a short ton or a net ton.  Do not confuse this with a long ton (also called a gross ton) or a metric ton (also spelled tonne), which have different measurement equivalents.







P1. Perform the following conversions:
(a) 1.4 meters to centimeters
(b) 218 centimeters to meters
(c) 42 inches to feet
(d) 15 kilograms to pounds
(e) 80 ounces to pounds
(f) 2 miles to kilometers
(g) 5 feet to centimeters
(h) 15.14 liters to gallons
(i) 8 quarts to liters
(j) 13.2 pounds to grams

P1. (a)

Cross multiply to get

(b)

Cross multiply to get
, or

(c)

Cross multiply to get
, or

(d) 
(e) 
(f) 

(g) 

(h) 

(i) 

(j)