The trick to solving these problems is constructing a conversion factor. It will benefit you to memorize some of the more common prefixes ordered from largest to smallest.
Prefix | Symbol | Power |
mega- | M | 10^{6} |
kilo- | k | 10^{3} |
hecto- | h | 10^{2} |
deca- | D | 10^{1} |
deci- | d | 10^{-1} |
centi- | c | 10^{-2} |
milli- | m | 10^{-3} |
micro- | 10^{-6} | |
nano- | n | 10^{-9 } |
pico- | p | 10^{-12} |
Metric-Metric Conversions
Example 1: Convert 2.50 mg to picograms.
Example 2: Convert 0.080 cg to kg.
1. Write 250 mg, then write a multiplication sign, a fraction bar, an equal sign, and the unit you are converting to.
2. Write the unit from the problem,mg, in the denominator of the conversion factor:
3. Write the unit you are converting to in the numerator of the conversion factor:
4. Look at the two prefixes in your conversion factor. Put a one in front of the larger one.
5. Calculate the difference between the two powers being used. In our case, -12 and -6 have a difference of 6. Write the power of the unit in the numerator as a positive exponent. In our example, 10^{6}.
6. Multiply and write your answer using scientific notation.
Here are the steps for example 2. For the conversion factor, the difference between ^{-}2 and 3 is 5.
Metric - Metric Practice Problems: (Answers at the end)
1. 0.75 kg to mg
2. 1500 mg to kg
3. 2390 g to kg
4. 0.52 kg to g
5. 65 kg to g
6. 750 mg to g
7. 0.25 Mg to cg
English-Metric Conversions
English-Metric conversions are calculated in the same way as metric-metric conversions only the conversion factors are different. It will benefit you to memorize a few conversion factors. Here's a sample:
2.54 cm = 1 inch
454 g = 1 lb
0.946 L = 1 qt
^{o}C = (^{o}F - 32)/1.8
Let's convert the mass of my 23 pound cat to kilograms. We can't convert this in one step because it is difficult to memorize every conversion factor for every possible scenario. First, we'll convert pounds to grams (a common conversion), then we'll convert grams to kilograms.
The key to conversion problems is to set up your conversion factors so that the units cancel out. If the units do not cancel out, your conversion factor is incorrect.
Metric-Metric Practice Answers:
1. 7.5 x 10^{5} mg
2. 1.5 x 10^{-}3 kg
3. 2.39 kg
4. 520 g
5. 6.5 x 10^{4} g
6. 7.5 x 10^{-}4 g
7. 2.5 x 10^{7} cg