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.