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Slide 2 Measurements and Calculations The SI System Slide 3 Systme Internationale d'Units (SI) an internationally agreed upon system of measurements. Decimal system (all conversions based on multiples of 10) SI consists of seven base units. Base Unit: defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units. Slide 4 1 mL = 1 cm 3 1 milliliter is the same volume as 1 cubic centimeter. 1 mL of water has a mass of approximately 1 g The mass of 1 milliliter of water is approximately 1 gram. 1 L of water has a mass of approximately 1 kg The mass of 1 liter of water is therefore approximately 1 kilogram. 1 m 3 of water has a mass of approximately 1 t There are 1000 liters in a cubic meter, so the mass of 1 cubic meter of water is approximately 1000 kilograms or 1 metric ton. Slide 5 Mass of a nickel is 5 g A US nickel weighs 5 grams, and a penny weighs 2.5 grams. A typical doorknob is 1 m high Although there's no precise standard for doorknob heights, they're often about 1 meter above the floor. Slide 6 The diameter of a CD or DVD is 12 cm A CD or DVD is 12 centimeters (120 millimeters) across. The diameter of the center hole is 15 millimeters. 1 ha is 100 2 m 2 1 hectare is 10 000 square meters, equivalent to the area of a square 100 meters on a side. A football field is about 100 meters long, so imagine a square the length of a football field on each side, and that's 1 hectare. Slide 7 Base Units The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.second The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second.meter The SI base unit of mass is the kilogram (kg), about 2.2 poundskilogram Slide 8 SI Base Units Slide 9 MANY DERIVED UNITS Quantity Unit Abbreviation Speed = Length/Time meter/second m/s Volume =(Length) 3 (meter) 3 m 3 Density = Mass/Volume kg/m 3 kg/m 3 Acceleration = speed/time m/s 2 m/s 2 Force = Mass x Acc kg m/ s 2 N (Newton) Pressure = Force/Area kg/m s 2 Pa (Pascal) Energy = Force x Length kg m 2 / s 2 J (Joule) Slide 10 PrefixSymbolExponential yottaY10 24 zettaZ10 21 exaE10 18 petaP10 15 teraT10 12 gigaG10 9 megaM10 6 kilok10 3 hectoh10 2 decada10 1 no prefix (base unit)10 0 decid10 1 centic10 2 millim10 3 micro 10 6 nanon10 9 picop10 12 femtof10 15 attoa10 18 zeptoz10 21 yoctoy10 24 Slide 11 Converting between SI Units Use the chart like this: 1 prefixed unit = exponential value of the prefix 1 cm = 10 -2 m 1 nm = 10 -9 m 1 Mm = 10 6 m Example: Slide 12 Measurements of Length Base Unit: the Meter Centimeter Millimeter Nanometer Micrometer Picometer Slide 13 Measurement of Mass Base Unit: the kilogram (the gram is too small) only prefixed base unit Measurement of Time Base Unit: the second Slide 14 Measurement of Temperature A measure of how hot or how cold something is A quantity that determines the direction of heat flow: warmer to cooler Three temperature scales commonly used: Celsius Kelvin (absolute) Fahrenheit Slide 15 To Convert F to C 1.8 degrees F = 1 degree C F = 32 + (1.8 x degrees C) Example: Convert 22 degrees C to degrees F C = F 32/1.8 Example: Convert 98.6 degrees F to degrees C. Slide 16 To Convert Celsius to Kelvin 0 degrees C = 273 K K = C + 273 C = K -273 Examples: Convert 100 degrees C to Kelvin. Convert 475 K to degrees C Convert 250 K to degrees C. Slide 17 Volume and Density Calculations Derived Units Slide 18 Volume Base Unit : m 3 Not practical because it is very large Commonly used: dm 3 Also called THE LITER (L) 1 dm = 10 cm 1 cm 3 = 1mL 1 dm 3 = 1 L NOTE: 1 dm 3 = (10 cm) 3 = 1000 mL= 1000 cm 3 = 1L Example: Calculate the volume of a cube that is 3.30 cm on each side. Slide 19 Density Mass to volume ratio The mass of a unit volume density = mass/volume d = m/v Slide 20 Examples Calculate the density of a piece of glass with a mass of 6.65 g and a volume of 2.95 mL. Calculate the thickness of an aluminum foil 15.38 cm long and 14.39 cm wide. The mass of the foil is 1.4939 g. The density of aluminum is 2.70 g/cm 3. (HINT: We consider the Aluminum foil to be a rectangular solid). Slide 21 Dimensional Analysis (Factor Label) Method of calculating using the units Makes word problems and chemistry calculations easy! Any unit can be converted to another by using appropriate conversion factors Start unit x final unit = final unit start unit Conversion factors (equalities written as fractions) Slide 22 Example On a picnic, 162 students are each given 2 hot dogs. If there are 9 hot dogs per pound, priced at $ 4 per 3 pounds, what is the cost of the hot dogs? Note that the following conversion factors can be obtained from the text of the problem: 1 student = 2 hotdogs 9 hot dogs = 1 lb $4 = 3 lbs To begin solving the problem, start with a known and keep your goal in mind: Note that all the units (except $) cancel out!