# 1.2 Measurement in Experiments

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

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

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

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

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

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

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?

Scientific Method A way of thinking and problem solving
A group of related processes and activities

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

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

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

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

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

How many significant figures?
x 103 x 10-4 x 107

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.

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

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

Equations Equations indicate relationships of variables

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?

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,