Return to Metric Table of Contents
A brief discussion of the basic metric units.
In order to properly convert from one metric unit to another, you must have the prefixes memorized. One good technique is to use flashcards. Here is a search for metric prefix flashcards. There is even someone selling an e-book for metric prefix flashcards.
Note for the future: you will need to determine which of two prefixes represents a bigger amount AND you will also need to determine the exponential "distance" between two prefixes. These skills will be necessary in order to correctly convert one metric unit to another.
A metric prefix is a modifier on the root word and it tells us the unit of measure. For example, centigram means we are count in steps of one one-hundredth of a gram, μg means we count by millionths of a gram.
A List of the Metric Prefixes
Multiplier | |||
Prefix | Symbol | Numerical | Exponential |
yotta | Y | 1,000,000,000,000,000,000,000,000 | 10^{24} |
zetta | Z | 1,000,000,000,000,000,000,000 | 10^{21} |
exa | E | 1,000,000,000,000,000,000 | 10^{18} |
peta | P | 1,000,000,000,000,000 | 10^{15} |
tera | T | 1,000,000,000,000 | 10^{12} |
giga | G | 1,000,000,000 | 10^{9} |
mega | M | 1,000,000 | 10^{6} |
kilo | k | 1,000 | 10^{3} |
hecto | h | 100 | 10^{2} |
deca | da | 10 | 10^{1} |
no prefix means: | 1 | 10^{0} | |
deci | d | 0.1 | 10¯^{1} |
centi | c | 0.01 | 10¯^{2} |
milli | m | 0.001 | 10¯^{3} |
micro | μ | 0.000001 | 10¯^{6} |
nano | n | 0.000000001 | 10¯^{9} |
pico | p | 0.000000000001 | 10¯^{12} |
femto | f | 0.000000000000001 | 10¯^{15} |
atto | a | 0.000000000000000001 | 10¯^{18} |
zepto | z | 0.000000000000000000001 | 10¯^{21} |
yocto | y | 0.000000000000000000000001 | 10¯^{24} |
For another presentation of these prefixes, please go here.
Problems concerning the units themselves
There are three items - name, symbol, and size - that must be known. Problems could give any one and ask for one or both of the others. Here are only some possible problems (of many):
I. Given either the name or the symbol of the prefix, give the other:
1) c 6) milli 2) k 7) femto 3) T 8) giga 4) μ 9) pico 5) d 10) hecto
A word to the wise: deca- (symbol = da) is a little used unit prefix. This makes it a prime target for teachers to test. Just sayin'.
II. Given the prefix size, give its name:
11) 10¯^{15}
12) 1,000
13) 10^{9}
14) 10¯^{2}
15) 0.000001
Problems concerning the exponential distance between two prefixes
This next set of problems deserves some comment. The reason is that this particular skill isn't really mentioned by chemistry (or physics) teachers. It seems that everybody just assumes students pick it up somewhere in a math class. It is an important skill that goes somewhat untaught, so I've decided to address it.
The skill I'm talking about is figuring out the absolute, exponential distance between two prefixes. For example, the absolute distance between milli and centi is 10^{1}. The distance between kilo and centi is 10^{5}.
What you should do is compare the two exponents as if they were placed on a number line made of exponents and the compute the absolute exponential distance between them. The key word is absolute. For example, someone might mentally do the distance between kilo and centi by comparing the exponents of positive 3 and negative 2 and getting one. So they reason the distance is 10^{1}. They would be wrong.
The absolute exponential distance between 3 and -2 is 5, not 1. Done as an exponent, the absolute exponential distance between kilo- and centi- is 10^{5}. In the problems to follow, the exponential form will be the one used. In other words, 10^{5} is used in the solution to the problem; the 5 by itself will never be used. The 5 is only used in descriptions about how to determine the distance. Repeat: you will use the proper exponential value (like 10^{5}) in a solution to a problem; you will NEVER use just the exponent (the 5) in a solution.
Here is a number line with the two prefixes in problem sixteen marked:
Compute the absolute, exponential distance between two given prefixes:
16) kilo and femto
17) milli and micro
18) micro and mega
19) centi and pico
20) nano and kilo
21) deci and tera
22) pico and micro
23) kilo and giga
24) femto and centi
25) milli and centi