Reading Scales & Significant Figures
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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.