Analyzing Data

Chapter 2

KEY TERMS

• Qualitative measurement – a measurement that gives descriptive nonnumerical results. (Qualities)

• Quantitative measurement – a measurement that gives definite, usually numerical results. (Quantities)

Qualitative or Quantitative?

• The product was a white powder

• 760 mL of Acetone was added to the flask

• The test tube smelled like rotten eggs

Units

• Systeme Internationale d’Unites (SI)

• Base Units and SI Prefixes– A defined unit in a system of measurement that

is based on an object or event in the physical world is called a base unit.

• time, length, mass, temperature

Temperature• degree of hotness or coldness• Kelvin Scale – the SI scale in which the freezing

point of water is 273 K and the boiling point is 373 K 0K is absolute zero.

K = oC + 273oC = K - 273

Derived Units

• Derived units are combinations of base units.– Volume– Density

Density

• Density = mass/volume

• If a sample of aluminum has a mass of 13.5g and a volume of 5.0 cm3, what is its density?

• 2.7 g/cm3

Density vs. Mass

• A large metal weight would be both dense and heavy.

Density vs. Mass

• A single balloon would be neither dense nor heavy.

Density vs. Mass

• A small metal weight would be dense, but not particularly heavy

Density vs. Mass

• Enough balloons will be heavy, but still aren't dense.

Scientific Notation

• A way to express very large or very small numbers efficiently

• Numbers are written as a coefficient and 10 raised to a power36,000 is written as 3.6 x 104

0.0081 is written as 8.1 x 10-3

Try some examples…

4000

4.0 x 103

0.00039

3.9 x 10-4

Conversion Factors

• A ratio of equivalent measurements, such as 100cm/1m, is called a conversion factor.

One of the best approaches to problem solving is dimensional analysis. Dimensional analysis is a way to solve problems using units of the measurements.

Conversion Factors

• How many meters are in 48 km?

• Conversion factor is: 1 km = 1000m

• 48 000 meters

UNCERTAINTY IN MEASUREMENTS

• Accuracy describes how close a measurement comes to the true value.

• Precision is how close a series of measurements are to one another.

Uncertainty

• Accurate, Precise, Neither, or Both?

Uncertainty

• Accurate, Precise, Neither, or Both?

Uncertainty

• Accurate, Precise, Neither, or Both?

Uncertainty

• Accurate, Precise, Neither, or Both?

Accepted versus Experimental

• The accepted value is the correct or “true” value of something.

• The experimental value is the value measured in the lab.

ERROR

• Error = accepted value minus experimental value

• Percent error = absolute value of error divided by accepted value, multiplied by 100%

Error Example

• A student tested the lab balance by taking the mass of an object known to weigh 50.0g. The student measured the mass to be 48.5g. What was the percent error in this measurement?

• 5.00%

Significant Figures

• every nonzero digit is significant• zeros appearing between nonzero digits are

significant• leftmost zeros appearing in front of nonzero digits

are not significant• zeros at the end of a number and to the right of a

decimal point are significant• zeros at the rightmost end of a measurement that

lie to the left of an understood decimal are not significant (placeholders)

The Arrow Method

• If the number does NOT have a decimal in it…– Shoot an arrow from right to left

870000

• If the number has a decimal in it…– Shoot an arrow from left to right

0.00404

SigFig Examples

• How many significant digits are in:

• 305.0?

• 107,800?

• 23?

• 0.0005?

Representing Data

• Graphs– Types – Slope– Interpreting

• Interpolation and Extrapolation