## Metric Units of Measurement

In science, we use the Metric System, also known as the International System of Units, because it makes unit conversions simpler. Converting between units in metric only requires moving the decimal point to the left or right since units all differ by powers of ten. Maybe it's because we've got 10 digits of our own to count on that humans settled on Base 10, but other number systems are possible and have been used. If metric seems strange to you because you're used to the American system of measurements we inherited from the English (which, by the way, even the English have mostly given up), remember that money is metric so you already have some real-world experience. Converting dollars into dimes or pennies is pretty easy math, and in metric, there are no nickels. Every unit is a 10x multiple of another. Ok, quickly, in your head, how many pennies are there in \$1.60? How many dimes? Now, quickly, in your head, how many fluid ounces are in 1.64 gallons. How many pints? How many inches are in 13 feet? I think you begin to see my point. America, Liberia and Myanmar are the only countries in the world that haven't gone metric. We're not in very good company! Our archaic system hurts our ability to sell our goods internationally. It causes us to crash space probes. And it just doesn't make any sense. But ever since Jimmy Carter, the idea of converting to metric has been politically too hot to touch. Too bad because, while switching is hard, there would be substantial long term benefits to the economy and the country.

The metric system is based on powers of ten.

Base Units (there are others, but these are the most commonly used)

 Measurement Unit Symbol length meter m mass gram g volume liter L time second s temperature Celsius C

Table 1: Metric units arranged from left (smallest) to right (biggest).

 Prefix nano- micro- milli- centi- deci- deca- hecta- kilo- mega- giga- Abbreviation n µ m c d D h k M G Factor 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109

Table 2: The same table tipped over on its side, with metric units arranged from bottom (smallest) to top (biggest).

 Prefix Abbreviation Factor (size) giga- G 1,000,000,000 x or 109 100,000,000 x or 108 10,000,000 x or 107 mega- M 1,000,000 x or 106 100,000 x or 105 10,000 x or 104 kilo- k 1,000 x or 103 hecta- h 100 x or 102 deca- D 10 x or 101 Base unit (no prefix) meters, grams, Liters, seconds 1 x or 100 deci- d 0.1 x or 10-1 centi- c 0.01 x or 10-2 milli- m 0.001 x or 10-3 0.0001 x or 10-4 0.00001 x or 10-5 micro- µ 0.000001 x or 10-6 0.0000001 x or 10-7 0.00000001 x or 10-8 nano- n 0.000000001 x or 10-9

Sample Problems:

Hint: For an answer in BIGGER units, move the decimal point LEFT. For an answer in SMALLER units, move the decimal point RIGHT.

Practice Question 1:

Convert one kilometer into centimeters.

Look at Table 1. kilo- and centi- are 5 positions apart. You want your answer in the smaller units, so move the decimal 5 places to the right.

1.0 kilometer is 100,000 centimeters

Practice Question 2:

Twelve milliseconds is how many seconds?

Look at Table 2. Seconds is a base unit. Seconds and milli-seconds are three positions apart. You want your answer in seconds, the bigger unit, so you will move the decimal point three places to the left.

12 milliseconds is 0.012 seconds

Further Investigation:

Unit Converter

Unit Conversion Tutorial

Scientific Notation

Making a Graph

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