Slide 2 Slide 1 of 48 Measurements and Their Uncertainty 3.1 3.1
Section 3.1-2 Significant Figures in Measurements Slide 3 Copyright
Pearson Prentice Hall Measurements and Their Uncertainty > Slide
2 of 48 Significant Figures in Measurements Why must measurements
be reported to the correct number of significant figures? 3.1 Slide
4 Copyright Pearson Prentice Hall Measurements and Their
Uncertainty > Slide 3 of 48 Significant Figures in Measurements
Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to
be 2.46 lb. The first two digits (2 and 4) are known. The last
digit (6) is an estimate and involves some uncertainty. All three
digits convey useful information, however, and are called
significant figures. The significant figures in a measurement
include all of the digits that are known, plus a last digit that is
estimated. 3.1 Slide 5 Copyright Pearson Prentice Hall Measurements
and Their Uncertainty > Slide 4 of 48 Significant Figures in
Measurements Measurements must always be reported to the correct
number of significant figures because calculated answers often
depend on the number of significant figures in the values used in
the calculation. 3.1 Slide 6 Copyright Pearson Prentice Hall
Measurements and Their Uncertainty > Slide 5 of 48 Rules for
Significant Figures Here are the rules to follow when determining
how many significant figures one has: 1.Look for a decimal place.
It will determine how you analyze the value. 2.If there is a
decimal place, do the following Atlantic/Pacific method: Start
counting from the left hand side (present or Pacific). Ignore zeros
at the beginning (left). Start counting at the 1 st non-zero digit
(1 9). Count all of the remaining digits (including zeros). These
are the significant digits. 3.1 Slide 7 Copyright Pearson Prentice
Hall Measurements and Their Uncertainty > Slide 6 of 48 Rules
for Significant Figures Start counting from the right hand side
(absent or Atlantic). Ignore zeros at the beginning (right). Start
counting at the 1 st non-zero digit (1 9). Count all of the
remaining digits (including zeros). These are the significant
digits. 3.1 If there is NO decimal place, due the following: Slide
8 Copyright Pearson Prentice Hall Measurements and Their
Uncertainty > Slide 7 of 48 Significant Figures Practice Q:
1,809,000 has how many significant digits? A: Since there is NO
decimal, begin counting from the right (RHS), skipping the zeros in
the beginning. So, you skip the 1 st three (3) zeros and start
counting from the 9. At this point, you count all of the remaining
digits. This means that you have four (4) significant figures. 3.1
Slide 9 Copyright Pearson Prentice Hall Measurements and Their
Uncertainty > Slide 8 of 48 Significant Figures Practice Q:
0.057010 has how many significant digits? A: Since there IS a
decimal, begin counting from the left (LHS), skipping the zeros in
the beginning. So, you skip the 1 st two (2) zeros and start
counting from the 5. At this point, you count all of the remaining
digits. This means that you have five (5) significant figures
including the 0 between the 7 and the 1 and the 0 at the end. 3.1
Slide 10 Copyright Pearson Prentice Hall Measurements and Their
Uncertainty > Slide 9 of 48 Significant Figures in Measurements
3.1 Slide 11 Copyright Pearson Prentice Hall Slide 10 of 48 Slide
12 Copyright Pearson Prentice Hall Slide 11 of 48 Slide 13
Copyright Pearson Prentice Hall Slide 12 of 48 Slide 14 Copyright
Pearson Prentice Hall Slide 13 of 48 Practice Problems for
Conceptual Problem 3.1 4 2 4 3 Slide 15 Copyright Pearson Prentice
Hall Measurements and Their Uncertainty > Slide 14 of 48
Significant Figures in Calculations How does the precision of a
calculated answer compare to the precision of the measurements used
to obtain it? 3.1 Slide 16 Slide 15 of 48 Copyright Pearson
Prentice Hall Measurements and Their Uncertainty > Significant
Figures in Calculations In general, a calculated answer cannot be
more precise than the least precise measurement from which it was
calculated. The calculated value must be rounded to make it
consistent with the measurements from which it was calculated. 3.1
Slide 17 Copyright Pearson Prentice Hall Measurements and Their
Uncertainty > Slide 16 of 48 3.1 Significant Figures in
Calculations Rounding To round a number, you must first decide how
many significant figures your answer should have. The answer
depends on the given measurements and on the mathematical process
used to arrive at the answer. Slide 18 Copyright Pearson Prentice
Hall SAMPLE PROBLEM Slide 17 of 48 3.1 Slide 19 Copyright Pearson
Prentice Hall SAMPLE PROBLEM Slide 18 of 48 3.1 Slide 20 Copyright
Pearson Prentice Hall SAMPLE PROBLEM Slide 19 of 48 3.1 Slide 21
Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 20 of 48 3.1
Slide 22 Copyright Pearson Prentice Hall Slide 21 of 48 Practice
Problems for Sample Problem 3.1 87.1 meters (round up the 7) 4.36 x
10 8 meters 1.55 x 10 -2 meters 9.01 meters (round up the 9) 1.78
meters x 10 -3 (round up the 8) 630 meters (round up the .55) Slide
23 Copyright Pearson Prentice Hall Measurements and Their
Uncertainty > Slide 22 of 48 3.1 Significant Figures in
Calculations Addition and Subtraction The answer to an addition or
subtraction calculation should be rounded to the same number of
decimal places (not digits) as the measurement with the least
number of decimal places. Slide 24 Copyright Pearson Prentice Hall
SAMPLE PROBLEM Slide 23 of 48 3.2 Slide 25 Copyright Pearson
Prentice Hall SAMPLE PROBLEM Slide 24 of 48 3.2 Slide 26 Copyright
Pearson Prentice Hall SAMPLE PROBLEM Slide 25 of 48 3.2 Slide 27
Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 26 of 48 3.2
Slide 28 Copyright Pearson Prentice Hall Slide 27 of 48 1. A
student reports the volume of a liquid as 0.0130 L. How many
significant figures are in this measurement? a.2 b.3 c.4 d.5 3.1
Section Quiz Slide 29 Copyright Pearson Prentice Hall Slide 28 of
48 Thats All Folks ! ! !
