Unit Outline--Topics

1
Unit Outline--Topics

• What is Physics?
• Branches of Science
• Science Terms
• Scientific models
• Measuring and Units
• Powers of Ten and conversions
• Graphing
• Experimental Design
• Science vs. Technology
• Analyzing in Physics

2
Main Topics

• Identifying and using significant figures
• Using scientific notation
• Converting

3
Significant Figures

• Significant figures are the method used to
  indicate the precision of your measurements.
• Significant figures are those digits that are
  known with certainty plus the first digit that is
  uncertain.
• If you know the distance from your home to school
  is between 12.0 and 13.0 miles, you might say the
  distance is 12.5 miles.
• The first two digits (1 and 2) are certain and
  the last digit (5) is uncertain.

4
Significant Figures
Section 2 Measurements in Experiments
Chapter 1

• It is important to record the precision of your
  measurements so that other people can understand
  and interpret your results.
• A common convention used in science to indicate
  precision is known as significant figures.
• Significant figures are those digits in a
  measurement that are known with certainty plus
  the first digit that is uncertain.

5
Significant Figures, continued
Section 2 Measurements in Experiments
Chapter 1
Even though this ruler is marked in only
centimeters and half-centimeters, if you
estimate, you can use it to report measurements
to a precision of a millimeter.
6
Rules for Determining Significant Zeros
Section 2 Measurements in Experiments
Chapter 1
7
Counting Significant Figures

• Examples
• 50.3 m
• 3.0025 s
• 0.892 kg
• 0.0008 ms
• 57.00 g
• 2.000 000 kg
• 1000 m
• 20 m
• Scientific notation simplifies counting
  significant figures.

8
Rules for Rounding in Calculations
Section 2 Measurements in Experiments
Chapter 1
9
Rounding

• Round to 3 figures
• 30.24
• 32.25
• 32.65000
• 22.49
• 54.7511
• 54.75
• 79.3500

10
Rules for Calculating with Significant Figures
Section 2 Measurements in Experiments
Chapter 1
11
Calculating with Significant Figures

• 97.3 5.85
• 123 x 5.35

12

• Identifying and using significant figures
• Using scientific notation
• Converting

13
SCIENTIFIC NOTATION

• Used by scientists and engineers to express very
  large and very small numbers.
• Changes by powers of ten
• Count decimal places either to the right or left

• Left is a positive exponent
• 1200 m (1.2 x 103 m)
• Right is a negative exponent
• 0.00012 m (1.2 x 10-3 m)

14
What is a power of ten?

• A power of ten represents a decimal place.
• One power of ten can mean ten times less or ten
  times greater.

• Examples
• 10 m and 1 m differ by one decimal place or one
  power of ten.
• 0.001 m and 0.00001 m differ by two decimal
  places or two powers of ten.

15
SCIENTIFIC NOTATION

• The very large measurement 310,000,000 m can be
  rewritten

number
3.1 x 108 m
10 multiplied by itself 8 times
16
SCIENTIFIC NOTATION

• The very small measurement 0.00000071 can be
  rewritten

7.1 x 10-7
number
1 divided by 10 multiplied by itself 7 times
1 107
17
SCIENTIFIC NOTATION AND YOUR CALCULATOR

• It is possible to compute using numbers written
  in scientific notation.
• Heres how its done For 3 x 108 x 85
• Enter the number 3
• Press 2nd and then the EE key. Some
  calculators (Casio) use the EXP key
• Enter 8 for exponent (press the -/ key if
  exponent is negative)
• Press multiplication key
• Enter 85
• Press to solve the problem
• Answer is 2.55 x 1010

18

• Identifying and using significant figures
• Using scientific notation
• Converting

19
Prefixes
20
Prefixes represent different powers of ten
http//images.encarta.msn.com/xrefmedia/aencmed/ta
rgets/illus/tab/T045196A.gif
21
Converting Units

• Build a conversion factor from the previous
  table. Set it up so that units cancel properly.
• Example - Convert 2.5 kg into g.
• Build the conversion factor
• This conversion factor is equivalent to 1.
• 103 g is equal to 1 kg
• Multiply by the conversion factor. The units of
  kg cancel and the answer is 2500 g.
• Try converting
• .025 g into mg
• .22 km into cm

22
Classroom Practice Problem

• If a woman has a mass of 60 000 000 mg, what is
  her mass in grams and in kilograms?
• Answer 60 000 g or 60 kg

23
Dimensional Analysis

• Dimensions can be treated as algebraic
  quantities.
• They must be the same on each side of the
  equality.
• Using the equation ?y (4.9)?t2 , what
  dimensions must the 4.9 have in order to be
  consistent?
• Answer length/time2 (because y is a length and
  t is a time)
• In SI units, it would be 4.9 m/s2 .
• Always use and check units for consistency.

24
How do I interpret the prefixes?

• 1 meter is 100 power
• 10 meters are 101 power
• milli- is 10-3 power or 0.001 m (three powers of
  ten less than 1 meter or three decimal places
  less)
• kilo- is 103 power or 1000 m (three powers of ten
  more than 1 meter or three decimal places
  greater)
• giga- is 109 power or 1,000,000,000 m (nine
  powers of ten more than one meter or nine decimal
  places greater)

25
Why Convert?

• To compare the results from measurements using
  different units, one unit must be converted into
  the other unit.

• Two basic types
• System conversions
• English to metric
• example inches to centimeters
• Power of ten conversions
• Change in prefix reflects powers of ten
• example meters to centimeters

26
How do you convert?

• Use the factor-label method (also called
  dimensional analysis)

• 1. decide what must be converted
• 2. select conversion factor
• 3. set up factoring equation
• 4. perform math and solve

27
Meters in a kilometer? 103 m 1 km 1000 m 1
km Meters in a millimeter? 10-3 m 1 mm 0.001 m
1 mm
28
Sample Problem
Section 2 Measurements in Experiments
Chapter 1

• A typical bacterium has a mass of about 2.0 fg.
  Express
• this measurement in terms of grams and kilograms.

Given mass 2.0 fg Unknown mass
? g mass ? kg
29
Sample Problem, continued
Section 2 Measurements in Experiments
Chapter 1
Build conversion factors from the relationships
given in Table 3 of the textbook. Two
possibilities are
Only the first one will cancel the units of
femtograms to give units of grams.