Significant Figures

1
Significant Figures
2
Significant Figures

• It makes no sense to record the waters volume in
  the graduated cylinder below as 7.5213 mL since
  the smallest increment on the graduated cylinder
  is 1.0 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.
3
Significant Figures

• When recording a measurement you write down all
  of the known digits and one estimated digit.
• These digits are called significant figures.

• 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.

4
Significant Figures

• If the measurement, 7.5 mL were converted to
  liters, then it would read 0.0075 L.

7.5 mL 0.0075 L
5
Significant Figures

• Since the two measurements are exactly the same,
  then they should both contain exactly the same
  number of significant figures.

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!

6
Significant Figures

• The three zeros in 0.0075 L are not significant
  to the measurement .

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.

7
Significant Figures

• Not all digits in a measurement are significant
  figures.

7.5 mL 0.0075 L

• So what digits are significant
• in a measurement?

8
Significant Figures

• The following rules are used to determine which
  digits are significant in a measurement
• All nonzero digits in a measurement are always
  significant!
• 4.184 J/goC 273 K
• All trapped (sandwiched) zeros (between two
  nonzero digits) are always significant.
• 101.3 kPa 1002 K

9
Significant Figures

• All leading zeros (zeros to the left of the first
  nonzero digit) are never significant.
• 0.053 nm 0.00973 g/cm3
• Do not confuse
• significant figures
• with
• holding place

10
Significant Figures

• 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

11
Significant Figures

• 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

12
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

13
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

14
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

15
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
• (b) 0.0053745 g (2) - _______________g
• (c) 1250 mm (4) - _______________mm

1.30
0.0054
1250.
16
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)
• (d) 12 cm2 (4) - _______________cm2
• (e) 1?1024 atoms (3) - _________________atoms
• (f) 975 J (2) - _______________J

12.00
1.00?1024
980
17
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)
• (g) 273.15 K (3) - _______________K
• (h) 21.099645 L (4) - _______________L
• (i) 250 J/g (2) - _______________J/g

273
21.10
250