Transcript Measurement and Significant Figures

In This Lesson:
Measurement
and Significant
Figures
(Lesson 3 of 6)
Stuff You Need:
Calculator
Today is Thursday,
February 2nd, 2017
Pre-Class:
Get your calculators and get ready.
Something else to do:
What would it mean if I told you that when it comes to
basketball, I’m not very accurate but I am very precise?
Last thing:
Today (or maybe next class) I will teach you how 5 x 5 = 30.
Today’s Agenda
• Measurement
• Significant Figures
• Where is this in my book?
– P. 62 and going for quite a few pages…
By the end of this lesson…
• You should be able to differentiate between
accuracy and precision.
• You should be able to determine which digits
of a number are significant.
Measurement
• Yes, in the world of chemistry, even a term
such a measurement has a distinct definition.
– A measurement is a quantitative observation that
consists of two parts:
• Number
• Scale (unit)
– If you leave out either one, I must deduct points.
• For example:
• 21 grams
• 6.63 x 10-34 Joule seconds
Uncertainty
• As it turns out, not every
measurement is perfectly
accurate.
• In any measurement there’s
a degree of uncertainty.
• For example, how many mL
do you see here?
– 53 mL sounds good, but you
can estimate one more digit.
52. 9 mL?
• (In this class, you should
estimate that extra digit)
http://www.jce.divched.org/JCESoft/Programs/CPL/Sample/modules/gradcyl/pic/00322409.jpg
Accuracy versus Precision
• In addition to uncertainty, measurements also can
be judged according to their accuracy or their
precision.
– What’s the difference?
• Accuracy is how close a measurement comes to
reality.
• Precision is how “repeatable” a measurement is
or the number of decimal places an instrument
measures.
– “60% of the time, it works every time.”
Accuracy versus Precision
High Accuracy,
High Precision
1.
2.
Low Accuracy,
High Precision
High Accuracy,
Low Precision
Low Accuracy,
Low Precision
3.
http://antoine.frostburg.edu/chem/senese/101/measurement/slides/img017.GIF
4.
Accuracy and Precision
• Suppose you have an electronic
balance that provides
measurements to two decimal
places.
– It’s certain to two. Other digits are
uncertain.
• If the balance always gives you the
same mass for the same object, it’s
precise.
• If it gives you the right mass, it’s
accurate.
– Are there ways in which it could be
accurate but not precise?
– How about precise but not accurate?
http://hxdzjs.net/uploadfile/20100601/20100601134741293.jpg
Pre-Class Part Deux
• Facebook was recently reported to have 1.6
billion users1.
– Is it exactly 1,600,000,000?
– Could it possibly be 1,600,000,001?
– Why is it okay to just say 1.6 instead of all the zeroes?
• If you needed to calculate the circumference of a
circle but you only knew the diameter was 8,
what would you do?
– Most of us would multiply by pi (π).
– How much is pi, again?
1Bloomberg
Business Week – March 24, 2016
Significant Figures
• Scientists need to be clear with one another about
how many digits to which they are rounding.
– In other words, they need to be clear about the level of
uncertainty they’re willing to accept.
– One scientist may say pi is 3.141, another may say
3.141592654.
• To determine how many digits your answer should
be, we use significant figures.
• Significant figures are the “digits that count” –
overall, they’re used as a special form of rounding.
– Also known as Significant Digits, or Sig Figs, or Sig Digs
4 Rules for Counting Sig Figs
1. If the number contains a decimal point, count
from right to left until only zeros or no digits
remain.
Examples: 20.05 grams
4 sig figs
7.2000 meters
5 sig figs
0.0017 grams
2 sig figs
4 Rules for Counting Sig Figs
2. If the number does not contain a decimal point,
count from left to right until only zeros or no
digits remain.
Examples: 255 meters
3 sig figs
1,000 kilograms
1 sig fig
Quick Interlude: Oceanic Sig Figs
• Here’s a way to remember Rules 1 and 2, although it
doesn’t work in Hawaii:
• If there is a decimal point present, count in the
direction of the Pacific (to the left).
• If the decimal point is absent, count in the direction
of the Atlantic.
4 Rules for Counting Sig Figs
3. For numbers in scientific notation (M x 10n),
count only the sig figs in the M number – use
rules 1 and 2 normally.
Examples: 1.40 x 10-16 cm
3 sig figs
2 x 105 g
1 sig fig
4 Rules for Counting Sig Figs
4. Exact numbers have an infinite number of
significant figures.
Rare in this class (usually for unit conversions).
1 inch = 2.54 cm exactly
1 dozen = 12 eggs-actly
Counting Sig Figs
How many significant figures in each of the following?
1.0070 m =
5 sig figs
17.10 kg =
4 sig figs
100,890 L =
5 sig figs
3.29 x 103 s =
3 sig figs
0.0054 cm =
2 sig figs
3,200,000. =
2 sig figs (the decimal point
needs digits after it to count)
Now for some practice…
• Significant Figures in Measurements and
Calculations
– Part I – choose 15.
• Difficult and/or Scientific Notation:
– 13, 14, 18-20
• The competition will be afterward!
Now for a break…
• Let’s take a look at some pretty interesting
uses of measurements (particularly in terms of
accuracy).
– Parallel Parking video.
Rules for Significant Figures in
Mathematical Operations
• Addition and Subtraction:
• The number of digits after the decimal point in the
result equals the number of digits after the decimal
point in the least precise measurement.
• Round the “end” normally.
6.8 + 11.964 =
6.8 + 11.964 = 18.764  18.8
Adding and Subtracting
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
Now for some practice…
• Significant Figures in Measurements and
Calculations
– Part II – choose 5.
– Part III – choose 3.
• Difficult and/or Scientific Notation:
– 28, 30
• The competition will be afterward!
Rules for Significant Figures in
Mathematical Operations
• Multiplication and Division:
• The number of significant figures in the result equals
the number of significant figures in the least precise
measurement used in the calculation.
• Round the “end” normally.
6.38 x 2.0 =
6.38 x 2.0 = 12.76  13 (2 sig figs)
Multiplying and Dividing
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3
0.02 cm x 2.371 cm
0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g x 2.87 mL
2.9561 g·mL
2.96 g·mL
23 m2
4.22 g/cm3
Now for some practice…
• Significant Figures in Measurements and
Calculations
– Part IV – choose 5.
– Part V – choose 3.
• Difficult and/or Scientific Notation (you must
try one of these):
– 45, 46, 48, 50, 51, 55
• The competition will be afterward!
Closure
• So, using sig fig rules, solve this problem:
• 5x5=?
• 5 x 5 = 30
• Now solve this one:
• 5.0 x 5.0 = ?
• 5.0 x 5.0 = 25.0
Closure Part Deux
• Try this one:
• 15 g x 4.0 g = ?
• 15 g x 4.0 g = 60 g…but it needs to be 2 sig figs!
• 15 g x 4.0 g = 60.0 g…is 3 sig figs!
• Write this down: When in doubt, make it
scientific notation (we’ll do this later).
• 6.0 x 101 g2
Final FYI
• What about something like percent error?
| Experiment al - Accepted Value |
Percent Error  (
)  100
Accepted Value
• You’re doing both subtraction and division, so
which rule(s) apply?
– The answer is that multiplication/division trump
addition subtraction.
• So use the “least number of sig figs” rule.
More sig fig practice:
Do this:
http://www.sciencegeek.net/Chemistry/taters/Unit0Sigfigs.htm
Then try 10:
http://science.widener.edu/svb/tutorial/sigfigures.html
Transition
• CrashCourse – Unit Conversion and Significant
Figures