Chapter 1.3: Measurement Measurements and Their Uncertainty The International System of Units Density Temperature
Scientific Notation “Writing a number as a power of 10.” Why? It makes very large and very small numbers more manageable to write and use. – Rule of thumb: Use when number is greater than 10 or smaller than 0.1 Or, you may always use it! The number of sig. figs are clearly shown in a measurement.
Scientific Notation How important is a change in the power of 10?power of 10 Diameter of Earth’s orbit around the sun ≈ 100,000,000,000 m = 1.0*10 11 m Diameter of an atom ≈ 0.0000000001 = 1.0*10 -10 m
1. Move the decimal point in the original number so that it is located to the right of the first nonzero digit. 2. Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved. 3. If the decimal point moves: To the left, the power of 10 is positive. To the right, the power of 10 is negative. Writing in scientific notation
Significant figures (“sig figs”): the digits in a measurement that are reliable (or precise). The greater the number of sig figs, the more precise that measurement is. A more precise instrument will give more sig figs in its measurements. Significant Figures Every measurement has some degree of uncertainty.
“PACIFIC” Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit. 40603.23 ft 2 0.01586 mL = 7 sig figs = 4 sig figs PACIFIC The “Atlantic-Pacific” Rule
When are digits “significant”? “ATLANTIC” Decimal point is ABSENT. Count digits from right side, starting with the first nonzero digit. 40600 ft 2 1000 mL 3 sig figs = 1 sig fig = ATLANTIC
0.00932 Decimal point present → “Pacific” → count digits from left, starting with first nonzero digit = 3 sig figs 4035 Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit = 4 sig figs 27510 Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit = 4 sig figs Examples
Sig. Figs. In Calculations And Scientific Notation In this class, use scientific notation for all numbers greater than 10 and smaller than 0.1 and write all calculations to the correct number of significant figures In this class, we WILL follow the sig. fig. rules for operations
Write the following measurements in scientific notation, then record the number of sig figs. 1. 789 g 2. 96,875 mL 3. 0.0000133 J 4. 8.915 atm 5. 0.94°C 7.89*10 2 g 9.6875*10 4 mL 1.33*10 -5 J 8.915 atm 9.4*10 -1 °C 3 sig figs 5 sig figs 3 sig figs 4 sig figs 2 sig figs Practice problems
Accuracy & Precision Precision: How closely individual measurements agree with each other The “fineness” of a measurement Accuracy: how closely individual measurements agree with the true or accepted value
Accurate or Precise? Precise! (but not accurate) What is the temperature at which water boils? Measurements: 95.0°C, 95.1°C, 95.3°C True value: 100°C
Accurate or Precise? Accurate! (it’s hard to be accurate without being precise) What is the temperature at which water freezes? Measurements: 1.0°C, 1.2°C, -5.0°C True value: 0.0°C
Accurate or Precise? Not Accurate & Not Precise (don’t quit your day job) What is the atmospheric pressure at sea level? Measurements: 10.01 atm, 0.25 atm, 234.5 atm True value: 1.00 atm
Accurate or Precise? Accurate & Precise (it’s time to go pro) What is the mass of one Liter of water? Measurements: 1.000 kg, 0.999 kg, 1.002 kg True value: 1.000 kg
A graduated cylinder: 50 100 mL Beaker 50 mL Graduated cylinder A beaker: 41.0 41.2 mL (3 sig figs = very precise) 40. mL (2 sig figs = not as precise)
Precision examples: To measure the time for a pencil to fall…compare a stopwatch and a wall clock. To measure the volume of a liquid…compare a graduated cylinder and a beaker. The stopwatch & graduated cylinder are more precise instruments…so the readings they produce will have more sig figs.
The Metric System – SI Units of Measurement History of S.I. The Prefixes The Base Units Length, Volume, Mass, Temperature, Density and Temperature
International System of Units Why was it organized? It is simple, being based on powers of 10. (like our number system) Every country in the world uses the metric system except the USA, Myanmar, and Liberia. By 2009, all products sold in Europe must use the metric system. No dual-labelling will be permitted. Visit U.S. Metric Association (USMA), Inc. for more info.U.S. Metric Association (USMA), Inc.
International System of Units Scientists use a set of measuring units called SI, or the International System of Units.
Metric Prefixes Metric Prefixes (pg. 17 Memorize) A metric prefix indicates how many times a unit should be multiplied or divided by 10. Sometimes units have to be converted to other units (grams to kilograms)
Derived Units Additional SI units, including volume and density, are called derived units. Derived units are made from combinations of base units.
Derived Units Combination of base units. Volume= length width height 1 cm 3 = 1 mL Density - mass per unit volume (g/cm 3 ) D = MVMV D M V
Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,220 g D M V
Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g D M V WORK : V = M D V = 25 g 0.87 g/mL V = 28.7 mL
Density You have a sample with a mass of 620 g & a volume of 753 cm 3. Find density. GIVEN: M = 620 g V = 753 cm 3 D = ? D M V WORK : D = M V D = 620 g 753 cm 3 D = 0.82 g/cm 3
Measuring Temperature Temp.- a measure of how hot or how cold something is [*Base unit is Kelvin (K)] Thermometer used to measure 2 most familiar scales: Celsius and Fahrenheit (Fahrenheit is not used in science) Water Boils: 100 o C; 212 o F Water Freezes: 0 o C; 32 o F
Measuring Temperature Temperature can be converted from Fahrenheit to Celsius to Kelvins. To convert: K = °C + 273.15 °F = (1.8 * °C) + 32 °C = (°F-32) 1.8 **Fahrenheit cannot be converted directly to Kelvins. 0 Kelvin-lowest possible temp that can be reached; 0K= -273.15 o C (ie. Absolute zero)