Measurements in Experiments
1.2 pp 10-19
Mr. Richter
Agenda
 Turn in Posters
 Warm-Up
 Discuss Energy Paragraphs
 Finish Yesterday’s Notes
 Questions about the Quiz?
 Introduction to the Metric
System
 Notes (Day 1):
 Measurement
 The Metric System (SI)
 Metric Prefixes and
Scientific Notation
 Day 2:
 Accuracy
 Precision
 Significant Figures
Objectives: We Will Be Able To…
 List basic SI units and the quantities they describe.
 Convert measurements into scientific notation.
 Distinguish between accuracy and precision.
 Use significant figures in measurements and calculations.
Warm-Up:
 There are 5280 feet in a mile. There are 1000 meters in a
kilometer.
 How many feet are in 4 miles?
 How many meters are in 4 kilometers?
For Tomorrow’s Quiz You Should:
 Review your notes
 Review the slides online
 Pay special attention to things I have repeated
 (Like vocab, objectives, homework problems…)
 Bring a sharpened pencil and be ready to go at the bell
tomorrow
Measurement
What are Measurements?
 Measurements tell us how much of what kind of stuff we
have.
 Measurements require two things:
 A quantity – how much
 A dimension (units) – what kind
 UNITS MATTER!
 My amount of wealth differs greatly if I have 30 million dollars or
30 million yen
 I can’t say “I live four away from here.” It only makes sense if I
say “four miles” or “four kilometers”.
Système Internationale (SI)
aka The Metric System
 All scientists and most countries use the SI or metric system.
 Why?
 Because it is easy to convert between large and small units.
 And to use scientific notation.
 The SI system has three base units (p. 11):
 Meter – length
 Kilogram – mass
 Second – time
 All other units are combinations or derivations of these three.
Metric Prefixes
 The SI uses metric prefixes and scientific notation to
accommodate extreme values of the base units.
 You will be required to memorize:
 nano micro milli
 centi
 kilo-
 mega-
Homework for Tonight
 p14 #1-5
Warm-Up
 Work by yourself in your
notes to answer each
question.
 How many meters is:
1. 42 kilometers
2. 4.2 kilometers
 Remember to think in terms
of being realistic: are
meters larger or smaller
than the original unit?
3. 0.42 kilometers
 If you can, try to do this from
memory; without the prefix
charts.
7. 4.2 centimeters
4. 4200 centimeters
5. 420 centimeters
6. 42 centimeters
Agenda
 Warm-Up
 Accuracy and Precision
 Review Quiz
 Significant Figures
 Set Up Portfolios
 Review Homework
 More On Metric
Conversions
 Scientific Notation
Objectives: We Will Be Able To…
 List basic SI units and the quantities they describe.
 Convert measurements into scientific notation.
 Distinguish between accuracy and precision.
 Use significant figures in measurements and calculations.
Converting with Metric Prefixes
(Another Method)
 1 mm = 10-3 m, therefore:
 Make sure units cancel out.
 Bad:
 To convert between units,  Good:
multiply by the conversion
factor.
Using Units
 Units must agree. A fancy way of saying
that the units used to express a
measurement must match.
 For example:
 Don’t use kilograms to measure length.
Duh.
 Sometimes people will use different units
of distance to measure the same thing, like
area. Avoid and convert:
 feet-meters
 centimeter-meters
Scientific Notation
Review
Scientific Notation
 Used in conjunction with metric prefixes to indicate the size
of a measurement.
 To convert to scientific notation:
 slide decimal point to the right of the first non-zero value
 0.000345  3.45
 267000  2.67000
 then multiply by a power of 10 to compensate for the shifted
decimal point
 0.000345  3.45 x 10-4
 267000  2.67000 x 105
Your Turn
 Convert the following values
into scientific notation:
 How did you do?
1. 4.2 x 103
1.
4200
2. 3.406 x 102
2.
340.6
3. 2 x 10-2
3.
0.02
4. 6.50 x 10-3
4.
0.00650
Warm-Up
 Express the following
 How did you do?
measurements in scientific
 3.46 x 102 m
notation:
 2.4 (or 2.40 or 2.400) x 103 g
 346 meters
 1.8 x 10-3 m/s
 2400 grams
 0.0018 meters/second
Scientific Notation
 The real reason for scientific notation: not just because
we’re sick of writing zeros.
 Scientific notation allows us to compare the sizes of numbers
almost instantaneously.
 Which number is bigger?
 23000000000000000 or 170000000000000000
 How much easier is it in scientific notation?
 2.3 x 1016 or 1.7 x 1017
Accuracy and Precision
Accuracy
 Describes how close a measured value is
to the true value of the quantity measured.
 Errors in accuracy come from:
 human error – incorrect use of instrument or
science
 using a tape measure incorrectly
 reading a thermometer at the wrong level
 instrument error – the device used to take a
measurement doesn’t work
 the tape measure or thermometer is
broken
Precision
 Refers to the degree of exactness with which a measurement
is made and stated.
 Errors in precision come from the limitations of an
instrument, not human error or calibration.
 For example: if the scale at the doctor’s office measures only
to the nearest kilogram, then the doctor cannot be expected
to state your mass to the nearest tenth of a kilogram.
Accuracy vs. Precision: Length
 The length of a 18-cm pencil is measured three
times with a ruler by three different people:
 The length is measured to be about 18 cm each
time: accurate but not precise.
 The length is measured to be 16.92 cm, 20.31 cm,
and 17.75 cm respectively: precise but not
accurate.
 The length is measured to be 17. 98 cm, 18.03 cm,
and 17.96 cm: both accurate and precise.
Significant Figures
What numbers matter? (Summary of rules pp. 17-19)
Significant Figures (SigFigs)
 Significant figures indicate the degree of precision with
which a measurement was taken.
 For example: 23 meters vs. 23.0 meters. What’s the
difference?
 The same number mathematically, but the latter is more precise.
The measurement was taken with a more precise instrument.
 Significant Figures comes down to: Which zeros don’t
matter?
 Any in front of non-zero digits: 0.0008
 Any at the end of a number but to the left of the decimal: 2000
Significant Figures and Scientific
Notation
 Scientific notation tells the difference between significant
and insignificant figures.
 For example: 200 could have 1 significant figure or 3.
 In scientific notation:
 200 = 2 x 102, or
 200 = 2.00 x 102
 It is easy to see which measurement is more precise written
in scientific notation.
Calculations with Significant Figures
 Adding: the sum should have the same number of digits to
the right of the decimal as the least precise measurement.
 250.4 + 112 ≠ 362.4 (indicates too much precision)
 250.4 + 112 = 362
 Multiplying: the product should have the same number of
significant figures as the least precise measurement.
 4.6 x 6.7 ≠ 30.82 (indicates too much precision)
 4.6 x 6.7 = 31
 Note: Your calculator doesn’t get sig figs.
Your Turn
 Try p. 28 #20, a-d
Wrap-Up: Did we meet our objectives?
 List basic SI units and the quantities they describe.
 Convert measurements into scientific notation.
 Distinguish between accuracy and precision.
 Use significant figures in measurements and calculations.
Homework
 Due Wed:
 p19 #1-4