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1.2 Measurement in Experiments

1.2 Measurement in Experiments. Learning Objectives. List basic SI units and quantities they describe Convert measurements to scientific notation Distinguish between accuracy & precision Use significant figures in measurements & calculations. Numbers as Measurements.

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1.2 Measurement in Experiments

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  1. 1.2 Measurement in Experiments

  2. Learning Objectives • List basic SI units and quantities they describe • Convert measurements to scientific notation • Distinguish between accuracy & precision • Use significant figures in measurements & calculations

  3. Numbers as Measurements • In science, numbers represent measurements • Numbers involve three things • Magnitude how much? • Dimensions length, mass, time • Units of what?

  4. The SI system • The standard measurement system for science • Base units • Basic units that are not a combination of some other units • Derived units • Are combinations of base units

  5. Base Units

  6. Derived units • Derived units are combinations of base units

  7. Prefixes indicate orders of magnitude (powers of 10)

  8. Converting Prefixes & Units • The main idea: multiply the given unit by a conversion factor yielding the desired unit • Conversion factor: a ratio of two units that is an equivalent to 1. • Example: convert millimeters to meters 1 mm x 10-3 m = 1 x 10-3 m 1 mm Practice 1A, #1-5

  9. Converting units of area and units of volume • How many cm2 are in 1 m2? • How many cm3 are in 1 m3? • How many in3 are in 1 L?

  10. Scientific Method A way of thinking and problem solving A group of related processes and activities http://www.sciencebuddies.org/science-fair-projects/overview_scientific_method2.gif

  11. Scientific Method: Important Terms • Law vs. Theory • Fact / Observation • Hypothesis • Experiment

  12. Accuracy & Precision • Accuracy • Nearness of a measurement to the true value • Precision • Degree of exactness or refinement of a measurement • Repeatability of a measurement

  13. Precision • describes the limit of exactness of a measuring instrument • Significant figures reflect certainty of a measurement • Figures that are known with certainty

  14. Significant Figures • Represent numbers known with certainty • because they are measured • plus one final estimated digit • Reflect the precision of an instrument or measurement • Must be reported properly • Require special handling in calculations

  15. Rules to determine significant digits 1. All non-zeros ARE 2. All zeros between non-zeros ARE 3. Zeros in front of non-zeros ARE NOT 4. Final zeros to right of decimal ARE • Final zeros without a decimal ARE NOT

  16. How many significant figures? • 50.3 20.001 • 3.0025 3426 • 0.892 210 • 0.0008 6.58 x 103 • 57.00 1.534 x 10-4 • 2.000000 2.00 x 107 • 1000 5000. • 20. 30

  17. Rules of calculating with significant figures • When adding & subtracting, final answer must have fewest decimal places present in the calculation. • When multiplying & dividing, final answer must have fewest significant digits present among the factors in the calculation. • Number of figures in a constant are ignored wrt sig figs.

  18. 1.3 Language of Physics • Physical quantities often relate to one another in a mathematical way • Data is collected in a table form • Data is graphed • to show relationship of independent & dependent variables • When time is a variable it is usually the independent (x) variable • Manipulated & responding variables

  19. Data Table and Graph

  20. Equations Equations indicate relationships of variables

  21. Evaluating Physics Equations: Dimensional Analysis • Can give you clues how to solve a problem • Can help check many types of problems because… • Dimensions can be treated as algebraic quantities • Example: derive a formula for speed • Example: How long would it take a car to travel 725 km at a speed of 88 km/h?

  22. Order of Magnitude Estimates • Physics often uses very large and very small numbers • Using powers of ten as estimates of the numbers can help estimate and check your answers • Example: from the previous problem,

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