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Measurement Metric system (National Assembly of France, 1790) International System of Units (SI, 1960) Derived units: combinations of fundamental units Ex. Speed (m/s)

Equipment for Measurement Length Volume Mass Time Temp

Scientific Notation Width of a human hair = 0.000008 m Coefficient Power of Ten: 10x Coefficient? 8 Power? 10-6 8 x 10-6 m

How many atoms of water are in a Lake Washington? Scientific Notation How many atoms of water are in a Lake Washington? 97,000,000,000,000,000,000,000, 000,000,000,000,000 atoms -or- 9.7 x 1037 atoms

Scientific Notation on Calculators Your calculator should work with scientific notation! Look for: EE EXP Note: 9.64 x 105 = 9.65 E5 Coefficient Power of Ten 2. x 10-8 = 2.E-8

Scientific Notation Conversion to a standard number 3.252 x 106 If power of ten is positive, move decimal point to the RIGHT (add zeros if necessary) 3252000 4.56 x 10-3 If power of ten is negative, move decimal point to the LEFT (add zeros if necessary) 0.00456

Measured Numbers Numbers obtained when you measure a quantity Estimate the final digit 1 2 6 5 4 3 4.8 in Read greater than 4 and less than 5; estimate last digit 1 2 6 5 4 3 4.84 in Read greater than 4.8 and less than 4.9; estimate last digit

Significant Figures All measured digits, including the estimated digit 4.84 cm 2045 g 2.333 x 10-5 L 50. s Zeros not significant in 2 situations: At the beginning of a decimal number At the end of a number without decimal point 4500 cm 0.0063 kg 0.05202 L

Exact Numbers A counted number (not measured!) Ex. # of students in this classroom A definition comparing two units in same measurement system Ex. 1 ft = 12 in Ex. 1 kg = 1000 g NOT considered as significant figures!

Significant Figures in Calculations In lab, at work, we measure things. Then what? The number of sig figs in measured numbers limits the number of sig figs in a calculated answer. You can’t have more detail in your answer than you have in your measurements Number of sig figs in answer depends on what type of calculations you performed

Sig Figs in Calculations Multiplication and Division: Final answer has the same number of sig figs as the measurement with the fewest significant figures Addition and Subtraction: Final answer has the same number of decimal places as the measurement with the fewest decimal places 24.64 x 3.2 = 78.848 79. 3.525 - 5.2 = -1.675 -1.7 3.525 + 6.475 = 10 10.000

Rounding Rules How do we limit the number of sig figs? Rounding! Look at first non-significant number (to be dropped) Is this number 4 or less? Is this number 5 or more? Round “down” Round “up” 2390.321 to 4 sig figs 2390. 0.0056194 to 2 sig fig 0.0056 688511 to 3 sig figs 689000

Prefixes Is it easier to write: 590000 g or 590 kg? 0.0004 g or 0.4 mg? Prefixes can be attached to units to increase or decrease size by a factor of 10 (multiply by 10 or divide by 10) Multiply by 10x Multiply by 10-x

Common Prefixes with SI Units

Equalities used in Measurements Equality: A relationship between two units that measure the same quantity Length: 1 m = 100 cm = 1000 mm Volume: 1 L = 10 dL = 1000 mL 1 dL = 100 mL Cubic centimeter: cc 1 cm x 1 cm x 1 cm = 1 cm3 1 cc = 1 cm3 = 1 mL

Volume Conversions 1 m3 = 1000 L If 1 cubic centimeter equals 1 mL, how many milliliters does 1 cubic meter equal? 1 m = 100 cm 100 cm x 100 cm x 100 cm = 1000000 cm3 1000000 cm3 = 1000000 mL 1 x 106 mL 1 m3 = 1000 L 1 x 103 L

Conversion Factors: Changing Between Units 1 hr = 60 min Conversion Factor: Metric Conversion Factor:

More Conversion Factors Metric Conversion Factors: Metric- U.S. System Conversion Factors: 1 kg = 2.20 lb 1 km = 0.621 mi

More Conversion Factors Standard equalities can be looked up in a table (Table 1.9 in your book, for example) Other equalities may be stated in a problem Examples: The average speed of cars driving on I-5 during rush hour is 11 mph. Equality: 11 miles = 1 hour One five pound bag of sugar costs $4.00. Equality: 1 bag = 5 lb = $4.00

Percents as Conversion Factors Percent means 1 per 100 Example: If a person is 20% body fat by mass, then: 20 kg fat = 100 kg body total

End of class Practice Questions How many sig figs are in each the following? 0.00500 L 53,069 s 0.00004715 m 0.509 kg Write the numbers above in scientific notation. How many sig figs does each have now? Write a conversion factor relating micrograms to grams

Practice Questions What is the temperature on each (˚C) thermometer shown? (sig figs!) 4.9 ˚C 61.5 ˚C Is each of the following an exact or measured number? The number of chair legs in this room The length of your benchtop in inches The length of your benchtop in cm The area of the projector screen Exact Measured Measured Measured

Using Conversion Factors Your patient tells you that she recently lost 15 kg. How many pounds has she lost? What’s given? What do we want to know? What conversion factors do I need? Set up problem weight lost (kg)= 15 kg weight lost (lb)= ? lb kg  lb 2.20 lb = 1 kg

Using Conversion Factors kg  lb 3. Set up problem 15 kg x ? Check sig figs!

Using Conversion Factors The recommended daily value of vitamin C is 60 mg. If an average orange contains 45 mg of vitamin C, how many oranges should you eat in a week? What’s given? What do we want to know? What conversion factors do I need? 1 week # of oranges week  # oranges  days  mg vitamin C

Physical Properties of Materials Physical Property: can be measured or perceived without changing the material’s identity Intensive Independent of amount of substance Ex. Boiling point Extensive Depends on amount of substance Ex. Mass, volume

Density Relationship between mass and volume Density is a physical property Density is an intensive property 4 times more mass 4 times more volume

Density Units: Density of water (at 20˚C and typical room pressure) SI: kg/m3 often use: g/L g/mL g/cm3 g/cc Density of water (at 20˚C and typical room pressure) 1 g/cc 1 g/mL

Density of Solids How can we determine the density of a solid? Need to know mass Need to know volume Measure displacement of water Does this method work for all solid materials?

Density Table Density can be used as a conversion factor! (relates mass to volume)

Specific Gravity (sp gr) Ratio between density of substance & density of water Measure sp gr with a hydrometer Units for sp gr? Unitless!

Temperature Measure of how hot or cold a substance is relative to another substance Scales and Units Scale Boiling Point H2O Freezing Point H2O Celsius ˚C Fahrenheit ˚F Kelvin K 100˚C 0˚C 212˚F 32˚F 373.15 K 273.15 K Note: the unit is not ˚K

Temperature Conversions How many units are between boiling point and freezing point of water? Scale Celsius ˚C Fahrenheit ˚F Kelvin K 100˚C – 0˚C = 100 units 212˚F – 32˚F = 180 units 373 K –273 K = 100 units the unit 1 Kelvin equals the unit 1 degree Celsius

Converting Units Fahrenheit to Units Celsius 180 Fahrenheit degrees = 100 Celsius degrees

Things to Remember about the Temperature Scales 0 K is absolute zero You can never (ever ever ever) have a temperature of negative K The unit for the Celsius scale is the degree C (˚C) The unit for the Fahrenheit scale is the degree F (˚F) The units for the Kelvin scale is the Kelvin (K) A change of x Kelvin = a change of x ˚C Start value and end values are different; Both changed the same amount (50 K units = 50 ˚C units)

Precision and Accuracy Precision: reproducibility Accuracy: how close to actual value Temp (˚C)