Return to Metric Table of Contents
In order to properly convert from one metric unit to another, you must have the prefixes memorized.
You will also need to determine which of two prefixes represents a bigger amount AND you will also need to determine the exponential "distance" between two prefixes.
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 brief discussion of the basic metric units.
A List of the Metric Prefixes
| Multiplier | |||
| Prefix | Symbol | Numerical | Exponential |
| yotta | Y | 1,000,000,000,000,000,000,000,000 | 1024 |
| zetta | Z | 1,000,000,000,000,000,000,000 | 1021 |
| exa | E | 1,000,000,000,000,000,000 | 1018 |
| peta | P | 1,000,000,000,000,000 | 1015 |
| tera | T | 1,000,000,000,000 | 1012 |
| giga | G | 1,000,000,000 | 109 |
| mega | M | 1,000,000 | 106 |
| kilo | k | 1,000 | 103 |
| hecto | h | 100 | 102 |
| deca | da | 10 | 101 |
| no prefix means: | 1 | 100 | |
| 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 |
Practice Problems
There are three items - name, symbol, and size - that must be known. Problems could give any one and ask for one of 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
2) k
3) T
4) μ
5) d
6) milli
7) femto
8) giga
9) pico
10) hecto
II. Given the prefix size, give its name:
11) 10¯15
12) 1,000
13) 109
14) 10¯2
15) 0.000001
This next set of problems deserves some comment. The reason is that this particular skill isn't really mentioned by teachers. It seems that everybody just assumes kids pick it up somewhere. Probably because it's a real easy skill, but it is important.
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 101. The distance between kilo and centi is 105.
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 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 3 and negative 2 and getting one. So they reason the distance is 101. They would be wrong.
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