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Measurements and Calculations The SI SystemSystme 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.1 mL = 1 cm31 milliliter is the same volume as 1 cubic centimeter.1 mL of water has a mass of approximately 1 gThe mass of 1 milliliter of water is approximately 1 gram.1 L of water has a mass of approximately 1 kgThe mass of 1 liter of water is therefore approximately 1 kilogram.1 m3 of water has a mass of approximately 1 tThere are 1000 liters in a cubic meter, so the mass of 1 cubic meter of water is approximately 1000 kilograms or 1 metric ton.

Mass of a nickel is 5 gA US nickel weighs 5 grams, and a penny weighs 2.5 grams.A typical doorknob is 1 m highAlthough there's no precise standard for doorknob heights, they're often about 1 meter above the floor.

The diameter of a CD or DVD is 12 cmA CD or DVD is 12 centimeters (120 millimeters) across. The diameter of the center hole is 15 millimeters.1 ha is 1002 m21 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.

Base UnitsThe SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.

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.

The SI base unit of mass is the kilogram (kg), about 2.2 pounds

SI Base Units

MANY DERIVED UNITSQuantity Unit AbbreviationSpeed = Length/Time meter/second m/sVolume =(Length) 3 (meter) 3 m 3Density = Mass/Volume kg/m 3 kg/m 3Acceleration = speed/time m/s 2 m/s 2Force = 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)Prefix Symbol Exponential yotta Y 1024 zetta Z 1021 exa E 1018 peta P 1015 tera T 1012 giga G 109 mega M 106 kilo k 103 hecto h 102 deca da 101 no prefix (base unit) 100 deci d 101 centi c 102 milli m 103 micro m 106 nano n 109 pico p 1012 femto f 1015 atto a 1018 zepto z 1021 yocto y 1024 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 = 106 m Example:

Measurements of Length Base Unit: the Meter CentimeterMillimeterNanometerMicrometerPicometer

Measurement of Mass Base Unit: the kilogram (the gram is too small) only prefixed base unit

Measurement of Time Base Unit: the second

Measurement of Temperature A measure of how hot or how cold something isA quantity that determines the direction of heat flow: warmer to cooler Three temperature scales commonly used: CelsiusKelvin (absolute)Fahrenheit

To Convert F to C and C to F 1.8 degrees F = 1 degree C F = 32 + (1.8 x degrees C) Example: Convert 22 degrees C to degrees F

C = F 32/1.8Example: Convert 98.6 degrees F to degrees C.

To Convert Celsius to Kelvin0 degrees C = 273 KK = C + 273 C = K -273Examples: Convert 100 degrees C to Kelvin.

Convert 475 K to degrees C

Convert 250 K to degrees C.

Volume and Density CalculationsDerived Units Volume Base Unit : m 3 Not practical because it is very largeCommonly used: dm 3 Also called THE LITER (L)1 dm = 10 cm1 cm 3 = 1mL 1 dm 3 = 1 LNOTE: 1 dm 3 = (10 cm) 3 = 1000 mL= 1000 cm 3 = 1LExample: Calculate the volume of a cube that is 3.30 cm on each side. Density Mass to volume ratioThe mass of a unit volume density = mass/volumed = m/v

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).

Dimensional Analysis (Factor Label)Method of calculating using the unitsMakes word problems and chemistry calculations easy!Any unit can be converted to another by using appropriate conversion factors

20Appropriate conversion factors Come from equality statements 1 kg = 103 g1 hr = 60 minutes 1 mm = 10-3 mConversion factors (equalities written as fractions)

Which factor do I use?Start unit x final unit = final unit start unit ExampleOn 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 hotdogs9 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!