7.1 Basic Terms and Conversions Within the Metric System 413 Table 7.1 Metric Prefixes Prefix Symbol Meaning kilo k 1000 basic unit × hecto h 100 basic unit × deka da 10 basic unit × — — basic unit (meter, gram, liter, . . .) deci d of basic unit 1 10 centi c of basic unit 1 100 milli m of basic unit 1 1000 MATHEMATICS TODAY Additional Metric Prefaces Why This Is Important We often deal with very large and very small quantities that may be stated using prefixes like giga, mega, micro, and nano. Information about the metric system is available through the National Institute of Standards and Technology website, NIST.gov. Two documents included on the website are the Metric Style Guide and A Brief History of Measurement Systems . The chart below gives the most commonly used prefixes and their symbols. METRIC PREFIXES Multiples Prefixes Symbols 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da * 100 10 1− deci d 10 2− centi c 10 3− milli m 10 6− micro μ 10 9− nano n 10 12 − pico p − 10 15 femto f 10 18 − atto a 10 21 − zepto z 10 24 − yocto y *Some countries use D for deka. Perform Conversions Within the Metric System We will use Table 7.2 to help demonstrate how to change from one metric unit to another metric unit using the meter as our basic unit. We could have also used gram, liter, or any basic unit of the metric system. Regardless of which basic unit we choose, the procedure is the same. For scientific work that involves very large and very small quantities, the following prefixes are also used: mega (M) is one million times the basic unit, giga (G) is one billion times the basic unit, tera (T) is one trillion times the basic unit, micro ( ,μ the Greek letter mu) is one millionth of the basic unit, nano (n) is one billionth of the basic unit, and pico (p) is one trillionth of the basic unit. For more information about the metric system and even more prefixes and symbols, visit the National Institute of Standards and Technology website: NIST.gov. In this book, the abbreviations or symbols for units of measure are not pluralized, but full names are. For example, 5 milliliters is symbolized as 5 m , not s 5 m . The millimeter is the smallest unit in the table. One centimeter is 10 times as large as one millimeter. One decimeter is 10 times as large as one centimeter. One meter is 10 times as large as one decimeter, and so on. Thus, converting from one unit in the metric system to another is a matter of multiplying or dividing by a power of 10. This means that we can do conversions within the metric system by moving the decimal point left or right as described in the following procedure. Table 7.2 Changing Metric Units Measure of length kilometer hectometer dekameter meter decimeter centimeter millimeter Symbol km hm dam m dm cm mm Number of meters 1000 m 100 m 10 m 1 m 0.1 m 0.01 m 0.001 m m Our neighbors in Canada (and also Mexico) use the metric system. CHANGING UNITS WITHIN THE METRIC SYSTEM 1. To change from a smaller unit to a larger unit (for example, from meters to kilometers), move the decimal point in the original quantity one place to the left for each larger unit of measurement until you obtain the desired unit of measurement. 2. To change from a larger unit to a smaller unit (for example, from kilometers to meters), move the decimal point in the original quantity one place to the right for each smaller unit of measurement until you obtain the desired unit of measurement. PROCEDURE
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