Transcript Reading Scales & Significant Figures

Unit 1- Units and
Measurement
Chemistry
Scientific Notation, Measurement,
Accuracy, Precision, Error
Scientific Notation
M x 10n
M
is the coefficient 1<M<10
 10 is the base
 n is the exponent or power of 10
 n is positive if number is greater 1
 n is negative if number is less 1
Scientific Notation
Write the following in scientific notation:
5450000 =
0.0002570 =
Limits of Measurement
 Accuracy
and Precision
 Uncertainty
 Exact Numbers vs. Inexact
 Accuracy
- a measure of how
close a measurement is to the
true value of the quantity being
measured.
Example: Accuracy
 Who
is more accurate when
measuring a book that has a true
length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
– a measure of how
close a series of measurements
are to one another. A measure of
how exact a measurement is.
 Precision
Example: Precision
Who is more precise when measuring
the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
Example: Evaluate whether the
following are precise, accurate or
both.
Error
Error= experimental –accepted value
Percent Error
% Error= |experimental –accepted| x100
accepted value
Significant Figures
The significant
figures in a
measurement
include all of the
digits that are
known, plus one
last digit that is
estimated.
 Uncertainty
Centimeters and Millimeters
The last (farthest to the right) significant figure in a
measured quantity always
has some associated uncertainty. The minimum
uncertainty is ± 1 in the last digit
Graduated Cylinder - Meniscus
Reading Scales to the Correct
Significant Figures Uncertainty?
Reading Scales to Correct
Significant Figures
Reading Scales to Correct
Significant Figures Uncertainty?
Rules for Counting Significant
Figures





All nonzero digits are significant. (42 has 2 sf’s.)
Zeros in the middle of a number are significant.
(4.803 cm has 4 sf’s.)
Leading zeros are not significant; they are there to
locate the decimal point. (0.00123 g has three sf’s.)
Trailing zeros are significant if the number contains
a decimal point. (55.220 K has five sf’s; 50.0 mg
has three sf’s, 5.100 × 10-3 has four sf’s.)
Trailing zeros are not significant if the number does
not contain a decimal. (34,200 m has three sf’s.)
How many sig figs?
100 kg
10302.00 cm
0.001L
10302 m
1.0302x104 ms
1010.010 g
0.000303 mm
92,900,000 km
6.02 x 1023 atoms
0.0205 m
2.05 x 10-2 m
Sig Figs in Addition/Subtraction
The result has the same number of
decimal places as the number in the
operation with the least decimal
places.
Ex: 2.33 cm
+3.0 cm
5.3 cm
Sig Figs in Multiplication/Division
 The
answer has the same sig figs as
the factor with the least sig figs.
 Ex: 3.22 cm
x 2.0 cm
6.4 cm2
Measured Numbers vs. Exact
Numbers


Exact numbers are values that are known
exactly (3 atoms = 3.00000…atoms) or that are
true by definition: 12 inches = 1foot, 60 s = 1
min, 5280 feet = 1 mile, 100 cm = 1m, 2.54 cm =
1 inch, etc.
All inexact or measured numbers will have
some limit to how precisely they are known, and
there is a limit to the number of significant digits
contained in the number.