Measurements and Calculations. The Scientific Method A logical approach to solving problems. 1....
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- Slide 1
- Measurements and Calculations
- Slide 2
- The Scientific Method A logical approach to solving problems.
1. Observation 2. Question/Problem 3. Hypothesis 4. Experiment 5.
Analyze 6. Communicate
- Slide 3
- Observations Use senses to obtain information. State the
facts!! No opinions! Qualitative = descriptive The liquid is clear
blue. Quantitative = numerical The liquid has a density of 1.21
g/mL.
- Slide 4
- Question/Problem What questions do you have? Does a problem
need to be solved? Formulate a Hypothesis Testable statement or
idea I think If, then
- Slide 5
- Experiment Test your hypothesis Take measurements Collect data
Analyze Results What does the data tell you? Patterns? Was the
question answered? Problem solved? Develop models & theories
Analysis can lead to more questions, too!!!
- Slide 6
- Communicate Publish results Confirmation from other
scientists
- Slide 7
- Measurement All measurements require a number and a unit. The
experiment requires 10.0 mL of ethanol. number = quantity of matter
unit = type of measurement
- Slide 8
- Significant Figures all certain digits plus the estimated digit
The measurement would be recorded as 1.75 cm. This measurement
contains 3 significant figures. (sig figs) certainestimated
- Slide 9
- The number of sig figs in a measurement is determined by the
precision of the measuring device. 0cm 1 2 3 4 0cm 40cm 1 2 3 4 3
cm 2.9 cm 2.95 cm 1 cm 1.1 cm 1.10 cm
- Slide 10
- Not all digits are significant!! Zeros are questionable! 1. All
digits 1-9 are sig. 2. ZEROs a) sandwich zeros = SIG b) at the end
of a number with a decimal point = SIG c) at the end of a number
without a decimal point = NOT SIG d) at the beginning of a number
with a decimal point = NOT SIG
- Slide 11
- How many sig figs are in the following measurements? 145.7
meters 10.4 kilograms 0.0053 liters 135.20 grams 250 milliliters
250. milliliters 0.0007250450 light years
- Slide 12
- Handling Measured Numbers and Math: Calculations and Sig Figs
The answer to a math problem cannot be more precise than the
measured numbers used to get the answer. Addition & Subtraction
Rules: Your answer should contain the fewest number of decimal
places as indicated by the measured numbers. Multiplication &
Division Rules: Your answer should contain the fewest number of sig
figs as indicated by the measured numbers.
- Slide 13
- Examples: 45.25 mL - 43.0 mL 132 g + 11.12 g 36.00 g 12.0 mL
(4.18 cm)(2 cm)
- Slide 14
- Units of Measurement: SI Base Units Type of Measurement
DefinitionUnit and abbreviation MassAmount of matter present gram,
g VolumeSpace occupied in 3 dimensions Liter, L DistanceSpace
between objects or points Meter, m TimePassage of eventsSecond, s
HeatThermal energyJoule, J TemperatureMolecular motionDegrees
Celsius, C Kelvin, K **Use reference paper for SI prefixes!
- Slide 15
- Unit Conversions: The Factor Label Method Given Quantity x
Conversion Factor(s) = Answer What is a Conversion Factor? a
fraction that shows how two measurements are numerically equal to
each other.
- Slide 16
- ex: 1000 milliliters = 1 Liter Conversion Factors would be..
ex: 365.25 days = 1 year Conversion factors would be:
- Slide 17
- Given Quantity x Conversion factor = Answer Ex: 25.6 mL = ? L
Ex: 2.90 years = ? days
- Slide 18
- Ex: 78 inches = ? m (1 inch = 2.54 cm) (100 cm = 1 m) Ex: 155
pounds = ? kilograms (1 lb = 454 g) (1000 g = 1 kg)
- Slide 19
- Ex: 10.0 miles per hour = ? meters per second (1 mile = 5,280
ft) (1 m = 3.28 ft) (1 hr = 60 min) ( 60 s = 1 min)
- Slide 20
- Derived Measurements measurements that are calculated from
other measurements Area = length x width Volume = length x width x
height Density = mass volume
- Slide 21
- Examples: 1. What is the area of a rectangle that measures
12.55 cm x 5.85 cm? 2. What is the density of a cube that measures
3.46 cm on each side and has a mass of 44.67 g? 3. The density of a
liquid is 1.15 g/mL. What volume of this liquid would have a mass
of 25.0 grams?
- Slide 22
- Scientific Notation writing a number as a multiple of 10 x.
1,6000.000000455 1.6 x 10 3 4.55 x 10 -7 Numbers greater than 1
will have a positive exponent. Numbers less than 1 will have a
negative exponent. You must keep one non-zero digit to the left of
the decimal point.
- Slide 23
- Ex: Write the number in scientific notation. 123,000 km =
_______________ 0.00078 g = ________________ Ex: Write the number
in standard form. 2.4 x 10 -2 L = _______________ 5.02 x 10 5 m =
_______________
- Slide 24
- Sci. Notation and Sig Figs the 10 x is NOT significant. 4.555 x
10 3 has ____sig figs 1.2 x 10 -4 has ____ sig figs 2.00 x 10 14
has ____ sig figs
- Slide 25
- Sci. Notation and Your Calculator: Every calculator is slightly
different. When possible use the EE or EXP button. 2.4 x 10 5
TYPE:2.4E5 or 2.4EXP5 Can also use 10 x, but you must put () around
entire number! 2.4 x 10 5 TYPE: (2.4 x 10 x 5)
- Slide 26
- Examples: 4.23 x 10 12 + 3.22 x 10 11 = 4.55 x 10 18 = 3.2 x 10
3 (5.4 x 10 -7 )(7.80 x 10 -3 ) =
- Slide 27
- Precision vs. Accuracy in Measurement Precision- how close
multiple measurements are to each other. the reproducibility of a
measurement. Accuracy how close a single measurement is to an
accepted value
- Slide 28
- Accuracy vs. Precision Accurate? Precise? Accurate ?
Precise?
- Slide 29
- Percentage Error Describes the accuracy of a measurement. %
error = (accepted value - experimental value) x 100 accepted value
% error can be a positive or a negative answer!!
- Slide 30
- example: A student measures and calculates the density of a
liquid as 1.35 g/mL. If the density of the liquid is actually 1.42
g/mL, what is the students percent error?
- Slide 31
- Proportions A proportion represents a relationship between two
measurements. Direct Proportion - as one variable increases, the
second variable increases. Inverse Proportion as one variable
increases, the second variable decreases.
- Slide 32
- Direct ProportionInverse Proportion