2: Measurement and Problem Solving

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• 2.1: Measurements
Chemists measure the properties of matter and express these measurements as quantities. A quantity is an amount of something and consists of a number and a unit. The number tells us how many (or how much), and the unit tells us what the scale of measurement is. For example, when a distance is reported as “5 kilometers,” we know that the quantity has been expressed in units of kilometers and that the number of kilometers is 5.
• 2.2: Expressing Numbers - Scientific Notation
Scientific notation is a system for expressing very large or very small numbers in a compact manner. It uses the idea that such numbers can be rewritten as a simple number multiplied by 10 raised to a certain exponent, or power.  Scientific notation expressed numbers using powers of 10.
• 2.3: Expressing Numbers - Significant Figures
Significant figures properly report the number of measured and estimated digits in a measurement. There are rules for applying significant figures in calculations.
• 2.4: The International System of Units
Recognize the SI base units. Combining prefixes with base units creates new units of larger or smaller sizes.
• 2.5: Problem Solving and Unit Conversions
During your studies of chemistry (and physics also), you will note that mathematical equations are used in a number of different applications. Many of these equations have a number of different variables with which you will need to work. You should also note that these equations will often require you to use measurements with their units. Algebra skills become very important here!
• 2.6: Solving Multistep Conversion Problems
Sometimes you will have to perform more than one conversion to obtain the desired unit.
• 2.7: Units Raised to a Power
Conversion factors for area and volume can also be produced by the dimensional analysis method. Just remember that if a quantity is raised to a power of 10 both the number and the unit must be raised to the same power of 10.
• 2.8: Density
Density is a physical property found by dividing the mass of an object by its volume. Regardless of the sample size, density is always constant.

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