The International System of Units and A Method of Problem Solving Called Dimensional Analysis

Transcription

1 The International System of Units and A Method of Problem Solving Called Dimensional Analysis If everyone is to understand what your measurements mean, you must agree on the units that will be used. By international agreement, a set of units called "The International System of Units" has been defined for scientific work. This system was adopted in 1960 by the General Conference on Weights and Measures. These units are also called metric units or SI units. Copyright Amy Brown Science Stuff Quantity Unit Name Unit Abbreviation Length meter m Mass kilogram kg Time second s or sec Temperature Kelvin K Amount of Substance mole mol Electric Current ampere A Luminous Intensity candela cd SI Units make measuring and calculating easier. Measurements are always expressed as decimals rather than fractions. It is very easy to change from one unit to another since they are based on 10. It is universally understood. 1

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3 centi- c hundredth (10-2 ) centi- c hundredth (10-2 ) milli- m thousandth (10-3 ) centi- c hundredth (10-2 ) milli- m thousandth (10-3 ) micro- µ millionth (10-6 ) 3

4 1000 mx = 1 X centi- c hundredth (10-2 ) milli- m thousandth (10-3 ) X = any unit micro- µ millionth (10-6 ) nano- n billionth (10-9 ) 100 cx = 1 X 1 kx = 1000 X X = any unit X = any unit 4

5 1/28/16 How many meters are in each of the following? 1 cx = 10 mx 1 Gm =? m 1 Mm =? m 1 km =? m 1 hm =? m 1 dam =? m? dm = 1 m? cm = 1 m? mm = 1 m?µm=1m? nm = 1 m X = any unit Metric Unit of Length The meter (m) is the SI base unit of length. Prefixes are used to indicate distances longer and shorter than a meter. What name and symbol is given to each of the following units of length? a) m b).001 m c).01 m d).1 m e) 10 m f) 1000 m Micrometer µm Millimeter mm Centimeter cm Decimeter dm Decameter dam Kilometer km 1,000,000,000 m 1,000,000 m 1,000 m 100 m 10 m 10 dm 100 cm 1,000 mm 1,000,000 µm 1,000,000,000 nm Metric Unit of Volume Volume: Is the space occupied by a sample of matter. The cubic meter (m3) is the SI derived unit for measuring volume. When chemists measure the volumes of liquids and gases, they often use a non-si unit called the liter. ml and cm3 The two units,, are interchangeable. 5

6 Metric Unit of Mass Mass: The quantity of matter an object contains. Weight: Mass and weight are often confused. Mass is not affected by gravitational pull. A measure of the pull by earth's gravity. Your weight on the moon would be less, but your mass on the moon would be the same. The is kilogram (kg) the SI base unit for measuring mass. Give the name and symbol for each of the following units: 1. A time that is 100 times as great as 1 second = 2. A length that is 1/1000 the length of 1 meter = 3. A mass that is 1000 times as great as 1 gram = 4. A mass that is 1/1,000,000 the mass of 1 gram = 1. Hectosecond (hs) 2. Millimeter (mm) 3. Kilogram (kg) 4. Microgram (µg) How large is: 1. centigram 2. millimeter 3. Kelvin 4. millisecond 1. Mass 2. Length 3. Temperature 4. Time 1. a kilogram, compared with a gram? 2. a millimeter, compared with a meter? 3. a centimeter, compared with a meter? 4. a nanogram, compared with a gram? 5. a decameter, compared with a meter? times larger 2. 1/1000 as large 3. 1/100 as large 4. 1/1,000,000,000 as large times larger 6

7 Conversion factors are numbers that are used to change from one unit to another. Conversion factors are formed from equalities that state a relationship between two units. For example: 1 kilometer = 1000 meters. When conversion factors are used properly, all units will divide out (or cancel out) EXCEPT the unit being converted to. Solving a Problem Using Dimensional Analysis How many kilometers are equal to 250 meters? 250 m 1 kilometer 1000 meters =.250 km When solving a problem using dimensional analysis, start with what you are given in the problem. Decide what conversion factor should be used in the next step. In the conversion factor step, place the unit on bottom that will cancel the unit in the previous step. Proceed until you are left with the unit you are looking for. Convert.044 km to meters.044 km 1000 m 1 km = 44 m Convert 696 cm 3 to m cm 3 (1) 3 m 3 = m 3 (100) 3 cm 3 Convert 4.6 mg to grams. How many seconds are in.079 years? 4.6 mg 1 g 1000 mg =.0046 g.079 yr 365 days 1 yr 24 hr 1 day 60 min 60 sec 1 hr 1 min = 2,491,344 sec 7

8 Convert.065 km to dm Convert 0.44 ml/min to microliters/sec.065 km 1000m 10 dm 1 km 1 m = 650 dm 0.44 ml min 1 L 1000 ml 1,000,000 µl 1 L 1 min 60 sec = 7.33 µl/sec The density of manganese is 7.21 g/cm 3. What is the density in kg/m 3? 7.21 g cm 3 1 kg 1000 g (100) 3 cm 3 (1) 3 m 3 = 7210 kg/m 3 There are 7 x 10 6 red blood cells in 1.0 mm 3 of blood. How many red blood cells are in one liter of blood? 7 x 10 6 cells (1000) 3 mm 3 (1) 3 m 3 1 cm ml 1.0 mm 3 (1) 3 m 3 (100) 3 cm 3 1 ml 1 L = 7 x cells/l 8