Unformatted text preview: MEASUREMENTS
Units and Prefixes Measurement Uncertainty Ch. 3 Significant Figures Scientific Notation Density Lab Dimensional Analysis Measurement Units of Measurement Measurements require? English system Metric system International System of Units (SI) Base units Mass (kilogram) Length (meter) Time (second) Temperature (kelvin) Amount (mole) Electric current (ampere) Mass vs. Weight Derived units: A combination of base units. Mass: a measure of the quantity of matter Weight: a force that measures the pull on a given mass by gravity Volume (cubic meter) Force (newton) Metric Prefixes: Allows the measurement to be written in a more compact way. Measurement Uncertainty Exact / Uncertain digits Digital displays Scales Use of + / Precision Accuracy (accepted value) “The Dartboard” Measurements are usually combined to be meaningful. Working with Numbers Significant Digits The uncertainty of the separate measurements must be reflected in the final result. Rules depend on keeping track of the significant digits in each measurement. Significant digits: The certain digits and the estimated digit of a measurement. Examples. A zero that is simply a place holder is not significant. Examples. The AtlanticPacific Rule Divides measurements into two kinds. Written with or without a decimal point. If the decimal is present, count from the Pacific side. If the decimal is absent, count from the Atlantic side. Start counting from the first nonzero digit you find. All to the end, including zeros are significant. 0.003579 / 567,043,000 / 0.02040 / 56,600. The AtlanticPacific Rule Divides measurements into two kinds. Written with or without a decimal point. If the decimal is present, count from the Pacific side. If the decimal is absent, count from the Atlantic side. Start counting from the first nonzero digit you find. All to the end, including zeros are significant. Significant Digits in Calculations
Follow the rules when combining measurements in a mathematical equation. When an exact number appears it is a definition, not a measurement. A definition has an infinite number of significant digits. Multiplication and Division
The measurement with the smallest number of significant digits determines how many digits are allowed in the final result. Calculators Example: 4.30m X 5.077m X 0.10m Addition and Subtraction The number of significant digits depends on the number with the largest uncertainty. Example: 975.0g + 1203g + 25.909g During calculations extra digits are carried in the intermediate results. Only the final answer is rounded to significant digits. Scientific Notation
Why? Scientific notation consists of two parts. The first part: a number between one and less than ten. The second part: a power of ten. Exponents. Converting Numbers to Scientific Notation
Movement of the decimal point. When the decimal point is moved to the right, the exponent is a negative number. When the decimal point is moved to the left, the exponent is a positive number. Examples: 0.00045; 34,000 Density One of the most important properties of matter. Equal to the mass of a substance per unit volume. D = mass / volume Dimensional Analysis Unit Measurement = Dimension Converting between units is called dimensional analysis. Unit equality is an equation that shows how different units are related. Example. Write a conversion factor from the unit equality. Example. A conversion factor will be an equation that is equal to 1. Using Conversion Factors
The unknown will go on one side of the equal sign. On the other side is the information you were given and a conversion factor. Select the correct conversion factor. Cancellation of units. Unit Conversions
Write down the units you need to convert. Find the conversion factor(s). Set up your equation. Fill in the known information. Solve for the correct value. Examples. ...
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 Fall '08
 petrovich
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