You may have experienced two types of measurement systems such as the metric and imperial systems. The imperial system consist of units such as inches, miles, or pounds. The metric system consists of units such as metres, grams, or litres.
The metric system is based on powers of 10 and each power has a prefix.
| Prefixes | |||
|---|---|---|---|
| Prefix Name | Prefix Symbol | Exponent of 10 | Value |
| zetta | Z | \(10^{21}\) | Sextillion |
| exa | E | \(10^{18}\) | Quintillion |
| peta | P | \(10^{15}\) | Quadrillion |
| tera | T | \(10^{12}\) | Trillion |
| giga | G | \(10^{9}\) | Billion |
| mega | M | \(10^{6}\) | Million |
| kilo | k | \(10^{3}\) | Thousand |
| hecto | h | \(10^{2}\) | Hundred |
| deka | da | \(10^{1}\) | Ten |
| \(10^{0}\) | One | ||
| deci | d | \(10^{-1}\) | Tenth |
| centi | c | \(10^{-2}\) | Hundredth |
| milli | m | \(10^{-3}\) | Thousandth |
| micro | \(\mu\) | \(10^{-6}\) | Millionth |
| nano | n | \(10^{-9}\) | Billionth |
| pico | p | \(10^{-12}\) | Trillionth |
| femto | f | \(10^{-15}\) | Quadrillionth |
| atto | a | \(10^{-18}\) | Quintillionth |
| zepto | z | \(10^{-21}\) | Sextillionth |
A method of moving left or right depending on the operation of divide or multiply can be used to move the decimal point operation with powers of 10.
Steps of the Practical Method:
Examples:
1. Convert \(25\, L\) to \(kL\).
\[25\, L = 0.025\, kL\]
2. Convert \(1.8\, cg\) to \(\mu g\).
\[1.8\, cg = 18,000\, \mu g\]
We can make a conversion by multiplying the given ratio that cancels the unwanted units and moves the decimal the correct number of places.
Examples:
1. Convert \(3.8\, hm\) to cm.
\[3.8\,hm \times \frac{10,000\,cm}{1\,hm} = 38,000\,cm\]
2. Convert \(9.01\, kL\) to daL.
\[9.01\,kL \times \frac{100\,daL}{1\,kL} = 901\,daL\]
