Transcript Lecture 1.06 - Significant Figures

Significant Figures
Significant Figures
• It makes no sense to record the water’s volume in
the graduated cylinder below as 7.5213 mL since
the smallest increment on the graduated cylinder
is 1.0 mL.
20 ml
15 ml
10 ml
5 ml
Only the digit “7” is truly known
and the digit “5” is estimated.
The other recorded digits (the "2",
the "1", and the "3") would have no
significance to the measurement
because they would be absolutely
complete guesswork.
Significant Figures
• When recording a measurement you write down
all of the known digits and one estimated digit.
• These digits are called significant figures.
20 ml
15 ml
10 ml
5 ml
• For example, if the volume of the
water in the graduated cylinder on
is recorded as 7.5 mL, then there
are two significant figures in the
measurement.
Significant Figures
• If the measurement, 7.5 mL were converted to
liters, then it would read 0.0075 L.
20 ml
15 ml
10 ml
5 ml
7.5 mL = 0.0075 L
Significant Figures
• Since the two measurements are exactly the
same, then they should both contain exactly the
same number of significant figures.
20 ml
15 ml
10 ml
5 ml
7.5 mL = 0.0075 L
• If the 7 and the 5 are the only
digits that are significant in
the 7.5 mL …
• … then the 7 and the 5 should
still be the only digits that are
significant in 0.0075 L!
Significant Figures
• The three zeros in 0.0075 L are not significant to
the measurement .
20 ml
15 ml
10 ml
5 ml
7.5 mL = 0.0075 L
• Of course the two zeros after
the decimal point are necessary
to hold the empty decimal places,
but they are not significant to the
measurement.
Significant Figures
• Not all digits in a measurement are significant
figures.
20 ml
15 ml
10 ml
5 ml
7.5 mL = 0.0075 L
• So what digits are significant
in a measurement?
Significant Figures
• The following rules are used to determine which
digits are significant in a measurement:
i. All nonzero digits in a measurement are
always significant!
4.184 J/goC
273 K
ii. All trapped (sandwiched) zeros (between
two nonzero digits) are always significant.
101.3 kPa
1002 K
Significant Figures
iii. All leading zeros (zeros to the left of the
first nonzero digit) are never significant.
0.00973 g/cm3
0.053 nm
• Do not confuse …
significant figures
with
holding place
Significant Figures
v. All trailing zeros (zeros to the right of the
last nonzero digit) are …
 always significant if a decimal point
appears in the measurement.
700. oC
40.00 g
 never significant if a decimal point does
NOT appear in the measurement.
700 oC
40 g
Significant Figures
v. When measurements are properly written in
scientific notation, all digits in the first factor
are always significant, including zeros.
3.00  108 m/s
2.99792458  108 m/s
1.60  108 J
1.602  108 J
Significant Figures
Ex.(1) Underline the digits that are significant in
the following measurements.
a) 1020μL
b) 0.0027 m
c) 10.0 g
d) 104000 µmol
Significant Figures
Ex.(2) Underline the digits that are significant in
the following measurements.
a) 98000 Pa
b) 10.01 g
c) 6170. mg
d) 0.00065 km/s
Significant Figures
Ex.(3) Underline the digits that are significant in
the following measurements.
a) 35.0 oC
b) 35.03 oC
c) 3200. ns
d) 2.060  104 mg
Significant Figures
Ex.(4) Report the following "calculator answers"
to the following final number of significant
figures. (The numbers in parentheses are the final
number of significant figures your answer should have)
(a) 1.29724 mol (3) - _______________mol
1.30
(b) 0.0053745 g (2) - _______________g
0.0054
(c) 1250 mm (4) - _______________mm
1250.
Significant Figures
Ex.(4) Report the following "calculator answers"
to the following final number of significant
figures. (The numbers in parentheses are the final
number of significant figures your answer should have)
2
(d) 12 cm2 (4) - _______________cm
12.00
(e) 11024 atoms (3) - _________________atoms
1.001024
(f) 975 J (2) - _______________J
980
Significant Figures
Ex.(4) Report the following "calculator answers"
to the following final number of significant
figures. (The numbers in parentheses are the final
number of significant figures your answer should have)
273
(g) 273.15 K (3) - _______________K
(h) 21.099645 L (4) - _______________L
21.10
(i) 250 J/g (2) - _______________J/g
250