|Metric Unit Prefixes|
|Prefix||Symbol||Scientific Notation||Number of
prefixes are what makes the metric system so easy to use. Doing
conversions between units with different prefixes is as easy as
moving the decimal point.
Base units include the meter (m), the gram (g), the liter (L), the second (s), the kelvin (K), and the mole (mol).
The SI unit of mass is the kilogram but the base unit for the purposes of this system of prefixes is the gram.
The prefix centi- does not follow the pattern of the other prefixes: it is 10x bigger than milli- and 100x smaller than the base unit. All other prefixes are 1,000x bigger or smaller than adjacent prefixes. It is only used for centimeters (cm). The prefixes hecto- (h), deka- (da), and deci- (d) have been left out because they are so seldom used.
|nano-||n||10-9||0.000 000 001|
|pico-||p||10-12||0.000 000 000 001|
|femto-||f||10-15||0.000 000 000 000 001|
We will concentrate on using the metric units chart (above) to create conversion factors. Conversion factors can be used as you learned to do for dimensional analysis. For example:
There are 1,000 mm (millimeters) in 1 m (meter) 1 m 4,350 mm × --------- = 4.35 m 1,000 mm
The old unit cancels out, giving a new unit.
First, we should review the metric units and how they are put together with the prefixes. See the chart at right for the commonly used units and what they measure. Prefixes are put in front of the names or abbreviations to create new units that measure either larger or smaller amounts. For example, a milliliter (mL) is smaller than a liter (L) and a kilometer (km) is larger than a meter.
To make a conversion factor from the metric units chart is easy. On the chart you will see that the unit prefixes all have a power of ten next to them. By counting the number of powers of ten between a pair of units on the chart you can tell how many of the smaller unit fit in one of the bigger unit. For example:
There are three powers of ten between the base unit (meter) and milli- (millimeter). meter: 100 millimeter: 10-3 0 — (-3) = +3 103 = 1,000 so 1 m = 1,000 mm
Here’s how you do it, step-by-step:
Here are two examples:
Convert kilograms to milligrams kg: 10+3 mg: 10-3 kg is the bigger unit so write: 1 kg = _____ mg do this: +3 — (-3) = +6 which means 1 × 106 mg so the conversion factor is 1 kg = 1 × 106 mg (1,000,000 mg) Convert millimeters to micrometers mm: 10-3 μm: 10-6 mm is the bigger unit so write: 1 mm = _____ μm do this: -3 — (-6) = +3 which means 1 × 103 μm so the conversion factor is 1 mm = 1 × 103 μm (1,000 μm)
The answers should always give you a positive power of ten when you do it this way because you should always expect to have a large number of small units for each big unit.
One thing that is helpful to notice is that most of the prefixes are three powers of ten away from their two nearest neighbors. It becomes as easy as counting by 3s: 3, 6, 9, 12, etc. The only exception in the chart provided here is centi- which is 10-2 and is one power of ten away from milli- and two powers of ten away from the base unit. So skip centi- most of the time (it’s only used for meters, anyway) and count by 3s.
Here is something that will help you decide whether your answers are correct after you do a conversion. If you are changing from a bigger unit to a smaller unit then the numerical answer will be bigger. If you are changing from a smaller unit to a bigger unit then the numerical answer will be smaller. For example:
1 × 106 mg 2.9 kg × --------- = 2.9 × 106 mg (or 2,900,000 mg) 1 kg So the number of mg equivalent to a certain numer of kg is a much larger number. 1 kg 510,000 mg × --------- = 0.51 kg 1 × 106 mg So the number of kg equivalent to a certain numer of mg is a much smaller number.
Do the following exercises on a separate piece of paper. Number each problem carefully and clearly.
Figure out how many of the first unit there are in the second unit then write a unit equality in the form 1 × 10–2 mentals = 1 centimental or 1012 picolos = 1 los
Convert each quantity into the units shown. For each calculation create the correct conversion factor using the metric units chart. Hint: you may have made a few of these conversion factors in the exercise above. Show work for the dimensional analysis calculation.