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