Study Guide: Metric Measurements
Place Value
The Metric System of Measures takes advantage of the fact that in the Decimal Number System it’s easy to multiply and divided by groups of 10. In the decimal system, the place (or position) of a symbol determines its value (the actual numeric quantity). In the below examples, the only thing that changes is the position of the symbol $1$, but the value of that symbol changes by multiples of $10$ from very large to very small.
\begin{array}{lrll} \hline Name & Value & Prefix & Symbol \\\ \hline trillion &1,000,000,000,000 & tera & T \\\ billion &1,000,000,000 & giga & G \\\ million &1,000,000 & mega & M \\\ thousand &1,000 & kilo & k \\\ hundred &100 & hecto & h \\\ ten &10 & deka & da \\\ unit &1 & & \\\ tenth &0.1 & deci & d \\\ hundredth &0.01 & centi & c \\\ thousandth &0.001 & milli & m \\\ millionth &0.000,001 & micro & ยต \\\ billionth &0.000,000,001 & nano & n \\\ trillionth &0.000,000,000,001 & pico & p \\\ \hline \end{array}
SI Metric System
The metric system is an international system of measurement. It has three main units:
| Unit | Symbol | Measures |
|---|---|---|
| Meter | m | length |
| Gram | g | mass (or weight) |
| Second | s | time |
Metric Linear
\begin{align} 10,mm &= 1,cm \\\ 100,cm &= 1,m \\\ 1000,m &= 1,km \\\ \end{align}
Metric Area
\begin{align} 100,mm^2 &= 1,cm^2) \\\ 10000,cm^2 &= 1, m^2) \\\ &= 1000000,m^2 \\\ \end{align}
Volume
\begin{align} 10,milliliters (ml) &= 1,centiliter (cl) \\\ 10,centiliters &= 1,deciliter (dl) = 100,milliliters \\\ 10,deciliters &= 1,liter (l) = 1,000,milliliters \\\ 10,liters &= 1,dekaliter (dal) \\\ 10,dekaliters &= 1,hectoliter (hl) = 100,liters \\\ 10,hectoliters &= 1,kiloliter (kl) = 1,000,liters \end{align}
Cubic
\begin{align} 1,000,cubic,millimeters (mm^3) &= 1,cu,centimeter,(cm^3) \\\ 1,000,cubic,centimeters &= 1,cu,decimeter,(dm^3) \\\ &= 1,000,000,cu,millimeters \\\ 1,000,cubic,decimeters &= 1,cu,meter (m^3) \\\ &= 1,stere \\\ &= 1,000,000,cu,centimeters \\\ &= 1,000,000,000,cu,millimeters \end{align}