Group Activity:
Metrics

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:

1. Identify the pair of units you need a conversion factor for and decide which one is the bigger unit. The bigger unit is always the one closer to the top of the chart.
2. Write down the bigger unit’s abbreviation next to the number 1. This is how many of that unit will be in your conversion factor.
3. Figure out how many powers of ten separate the two units.
4. Write down 1 × 10^x next to the smaller unit’s abbreviation, where the x is the difference in powers of ten.

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.

Exercises

Do the following exercises on a separate piece of paper. Number each problem carefully and clearly.

How Many Blank in a Blank?

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.