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## The Metric System

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**Units, Definitions and History**The Metric System**History**The disparate measurement system was one of the most frequent causes of disputes amongst merchants and between citizens and tax collectors across Europe. Leaders of the French revolutionary governments decided a new system was need. 1791: first official adoption of a universal measuring system. 1799: final proclamation of metric system placed in the Archives of the Republic. Today, 95% of the world’s population live in metricated countiries.**SI Units**Seven base units in SI Time (second) Length (meter) Mass (kilogram) Temperature (Kelvin) Amount of a substance (mol) Electric current (ampere) Luminous intensity (candela)**SI Units Cont.**Derived units in SI Volume: derived unit is the cubic meter (m3); cubic centimeter is more commonly used (cm3). For liquids, the liter is used; 1 L = 1 dm3. Density: ratio that compares the mass of an object to its volume. The units for density are often expressed as g/cm3**Prefix**Symbol Factor S.N. Example giga G 1 000 000 000 109 Gigameter (Gm) mega M 1 000 000 106 Megagram (Mg) kilo k 1 000 103 Kilometer (km) deci d 1/10 10-1 Deciliter (dL) centi c 1/100 10-2 Centimeter (cm) milli m 1/1000 10-3 Milligram (mg) micro µ 1/1 000 000 10-6 Microgram (µg) nano n 1/1 000 000 000 10-9 Nanometer (nm) pico p 1/1 000 000 000 000 10-12 Picometer (pm) Prefixes Used with SI Units**A technique for converting from one unit to another**Dimensional Analysis**Conversions WITHIN the Metric System**• You can simply move the decimal point... • But you have to know how to move it!!**Metric Unit Conversions**• Use this to remember the metric prefixes: “King Henry Died By Drinking Chocolate Milk • The first letters represent the prefixes (kilo, hecto, deca, base, deci, centi, milli)**Example**• It is common for runners to do a “10K” run. This means they are running 10 kilometers. How many millimeters is that? A lot!!!**Answer**• Look at the staircase graphic... • Start on the prefix “kilo” • Move down the staircase 6 steps (don't count the step you start on) to get to the prefix “milli” • This means you move the decimal point 6 places to the RIGHT 10 km is converted to 10,000,000 mm**Beyond the Metric System**• If you need to convert to or from units that are NOT metric units, we use a unit conversion technique called... “dimensional analysis” D.A.**Conversion Factors**• In dimensional analysis, we make conversion factors into fractions that we will multiply by. • For example, one conversion factor is: 1 inch = 2.54 cm • We can make two fractions out of this... 1 inch OR 2.54 cm 2.54 cm 1 inch**Example**• A pencil is 17.8 cm long, what is its length in inches? • Start with the “given”: 17.8 cm • Multiply by the “conversion factor” 17.8 cm x 1 inch = 2.54 cm**Example**• A pencil is 17.8 cm long, what is its length in inches? • Cross cancel “like” units: 17.8 cm x 1 inch = 2.54 cm**Example**• A pencil is 17.8 cm long, what is its length in inches? • Do the math using the correct number of significant figures (based on given information) 17.8 cm x 1 inch = 7.01 in. 2.54 cm**Which number goes on top and bottom in the conversion**factor? • Usually... • The unit you WANT goes on TOP • The unit you want to CANCEL goes on BOTTOM**Example**• A pencil is 8.1 inches, how many cm is it? 8.1 inches x 2.54 cm = 21 cm 1 inch The unit we WANT is cm so we put 2.54 cm on TOP of the conversion factor.**Multi-Step Example**• Sometimes, we must “string” several conversion factors together to get from one unit to another. • Ex. Mrs. DeLong's class is 47 minutes long. How many days long is this???**Multi-Step Example**• Need to go from minutes to hours to days 47 min x 1 hr x 1 day = 60 min 24 hrs Notice how “like” units can be cross-canceled.**Multi-Step Example**• Need to go from minutes to hours to days 47 min x 1 hr x 1 day = 0.033 days 60 min 24 hrs Notice how “like” units can be cross-canceled.