1. • August 27,2014
• 4th period Class starter:
Using your book, Define qualitative and
quantitative. Give an example of each.
5th period class starter:
Make 5 qualitative descriptions about
the room. Make 5 quantitative
descriptions about the room.
5. Derived Units
• A unit that is defined by a combination of
base units is called a derived unit.
6. Derived Units (cont.)
• Density is a derived unit, g/cm3, the
amount of mass per unit volume.
• The density equation is
density = mass/volume.
7. • Error is defined as the difference between
and experimental value and an accepted
value.
8. • The error equation is
error = experimental value – accepted value.
• Percent error expresses error as a
percentage of the accepted value.
9. Scientific Notation
• Scientific notation can be used to express
any number as a number between 1 and
10 (the coefficient) multiplied by 10 raised
to a power (the exponent).
• Count the number of places the decimal point
must be moved to give a coefficient between
1 and 10.
10. Scientific Notation (cont.)
• The number of places moved equals the
value of the exponent.
• The exponent is positive when the decimal
moves to the left and negative when the
decimal moves to the right.
800 = 8.0 ´ 102
0.0000343 = 3.43 ´ 10–5
11. Significant Figures
• Often, precision is limited by the tools
available.
• Significant figures include all known digits
plus one estimated digit.
12. Significant Figures (cont.)
• Rules for significant figures
– Rule 1: Nonzero numbers are always significant.
– Rule 2: Zeros between nonzero numbers are
always significant.
– Rule 3: All final zeros to the right of the decimal
are significant.
– Rule 4: Placeholder zeros are not significant. To
remove placeholder zeros, rewrite the number in
scientific notation.
– Rule 5: Counting numbers and defined constants
have an infinite number of significant figures.
13. Rounding Numbers
• Calculators are not aware of significant
figures.
• Answers should not have more significant
figures than the original data with the fewest
figures, and should be rounded.
14. Rounding Numbers (cont.)
• Rules for rounding
– Rule 1: If the digit to the right of the last significant
figure is less than 5, do not change the last
significant figure.
– Rule 2: If the digit to the right of the last significant
figure is greater than 5, round up to the last
significant figure.
– Rule 3: If the digits to the right of the last significant
figure are a 5 followed by a nonzero digit, round up
to the last significant figure.
15. Rounding Numbers (cont.)
• Rules for rounding (cont.)
– Rule 4: If the digits to the right of the last significant
figure are a 5 followed by a 0 or no other number at
all, look at the last significant figure. If it is odd,
round it up; if it is even, do not round up.
16. Rounding Numbers (cont.)
• Addition and subtraction
– Round numbers so all numbers have the same
number of digits to the right of the decimal.
• Multiplication and division
– Round the answer to the same number of significant
figures as the original measurement with the fewest
significant figures.
17. Graphing
• A graph is a visual display of data that
makes trends easier to see than in a table.
18. Graphing (cont.)
• A circle graph, or pie chart, has wedges
that visually represent percentages of a
fixed whole.
19. Graphing (cont.)
• Bar graphs are often used to show how a
quantity varies across categories.
20. Graphing (cont.)
• On line graphs, independent variables are
plotted on the x-axis and dependent
variables are plotted on the y-axis.
21. Graphing (cont.)
• If a line through the points is straight, the
relationship is linear and can be analyzed
further by examining the slope.
22. Interpreting Graphs
• Interpolation is reading and estimating
values falling between points on the graph.
• Extrapolation is estimating values outside the
points by extending the line.
