3 Metric Prefixes
Powers of 10 are also used in the metric system, which is commonly used by scientists. Metric prefixes are used before the base metric unit. The units for some quantities commonly measured in chemistry are shown below:
| Quantity | Unit | Abbreviation |
| mass | gram | g |
| time | second | s |
| length | meter | m |
| volume | liter | L |
| energy | Joule | J |
Using Standard Definitions
Metric prefix definitions are often shown in texts in the following format.
| 106 | mega | M |
| 103 | kilo | k |
| 10-1 | deci | d |
| 10-2 | centi | c |
| 10-3 | milli | m |
| 10-6 | micro | µ |
Since the prefix kilo means 103, a kilometer means 103 meters or 1000 meters:
1 km = 103 m or 1 km = 1000 m
Notice that the 103 or 1000 isn’t placed on the same side of the equals sign as the k, it’s on the opposite side of the equals sign. For example, 103 km = 1 m is wrong. You will need to know many metric prefixes and be able to correctly write the equality between the prefixed unit (km, in this case) and the no-prefix unit (m, in this case). Suppose you need the equality between Mg and g, so you need to put in the numbers in this equality:
___ Mg = ___ g
Put a 1 in front of the prefixed unit (Mg, in this case), then the number the prefix means in front of the no-prefix unit (g, in this case).
1 Mg = 106 g
One way to think about it is that when you remove the M prefix from the left side, you will have to replace it with the number that M means (106) on the right side. Again, don’t write the definition and the prefix on the same side. For example, 106 Mg = 1 g is wrong.
Example 3.1
What numbers should be placed in the blank spaces in the following:
___cm = ___m
Answer: Put the 1 in front of the unit containing the prefix (which is cm in this case). Then the definition of the prefix (10-2 in this case) goes in front of the no-prefix unit.
1 cm = 10-2 m
Example 3.2
What numbers should be placed in the blank spaces in the following:
___L = ___dL
Answer: Put the 1 in front of the unit containing the prefix (which is dL in this case). Then the definition of the prefix (10-1 in this case) goes in front of the no-prefix unit.
10-1 L = 1 dL
Using Definitions with Positive Exponents Only
As we have seen, 1 cm = 10-2 m. However, this isn’t the only way we can write the equality. If we multiply both sides by 102, we will have the following true equality
102 cm = 1 m or 100 cm = 1 m
Centi means 10-2. If we put that in front of the cm the equality is wrong. However, if we put 102 (note positive exponent) in front of the cm the equality is true.
So when you memorize the prefix definitions, you can either remember the table as given earlier, or you can put all powers as positive and remember if the prefix means bigger or smaller than the base unit. In the table below, X represents the base unit.
| 1 MX = 106 X | 106 in front of X because Mega is bigger than the base |
| 1 kX = 1000 X | 1000 in front of X because kilo is bigger than the base |
| 10 dX = 1 X | 10 in front of dX because deci is smaller than the base |
| 100 cX = 1 X (think 100 cents = 1 dollar) | 100 in front of cX because centi is smaller than the base |
| 1000 mX = 1 X | 1000 in front of mX because milli is smaller than the base |
| 106 µX = 1 X | 106 in front of µX because micro is smaller than the base |
Using the prefixes defined in this way, when trying to determine which numbers go where, first decide which is the bigger unit and put a 1 in front of it. Then think, “lots of small things equals one big thing,” and place the big number in front of the small unit. For example, L is bigger than cL, so put a 1 in front of L. Lots of cL equals 1 L, where the “lots of” is 100 because centi means 100 times smaller .
100 cL = 1 L
Example 3.3
Write the equality between µJ and J.
Answer: Since micro (µ) means 106 times smaller, a J is bigger than a µJ . Put a 1 in front of J (the big thing) and the 106 in front of the µJ (the small thing), since one big thing equals lots of small things:
1 J = 106 µJ
Example 3.4
Write the equality between kg and g.
Answer: Since kilo means 1000 times bigger, kg is bigger than g. Put a 1 in front of kg (the big thing) and the 1000 (or 103) in front of the g (the small thing), since one big thing equals lots of small things.
1 kg = 1000 g
