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**1.2 Measurement in Experiments**

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**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

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**Numbers as Measurements**

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

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**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

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**Base Units Physical Quantity (Dimension) Unit Abbreviation Mass**

Kilogram kg Length Meter m Time Second s Electric current Ampere A Temperature Kelvin K Luminous intensity Candela cd Amount of substance Mole mol

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**Derived units Derived units are combinations of base units Base Unit**

m (length) m3 (volume) kg (mass) s (time) N (newton) for force 1N = 1 kg∙m s2

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**Prefixes indicate orders of magnitude (powers of 10)**

Abbrev 10 -18 atto- a 10 -1 deci- d 10 -15 femto- f 10 1 deka- da 10 -12 pico- p 10 3 kilo- k 10 -9 nano- n 10 6 mega- M 10 -6 micro- μ 10 9 giga- G 10 -3 milli- m 10 12 tera- T 10 -2 centi- c 10 15 peta- P

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**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 m = 1 x 10-3 m 1 mm Practice 1A, #1-5

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**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?

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**Scientific Method A way of thinking and problem solving**

A group of related processes and activities

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**Scientific Method: Important Terms**

Law vs. Theory Fact / Observation Hypothesis Experiment

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**Accuracy & Precision Accuracy Precision**

Nearness of a measurement to the true value Precision Degree of exactness or refinement of a measurement Repeatability of a measurement

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**Precision describes the limit of exactness of a measuring instrument**

Significant figures reflect certainty of a measurement Are figures that are known because they are measured

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

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**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

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**How many significant figures?**

x 103 x 10-4 x 107

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**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 in the calculation. Number of figures in a constant are ignored wrt sig figs.

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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

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**Data Table and Graph Determining k through displacement x (m)**

Force (N) mass (kg) 0.00 0.01 0.49 0.05 0.03 0.98 0.10 0.06 1.47 0.15 0.09 1.96 0.20

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Equations Equations indicate relationships of variables

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**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?

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**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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