Transcript Uncertainty in Measurement: Significant Figures


Every measurement we make includes some
uncertainty.
 We can never measure something exactly or know
a quantity with absolute certainty.

The numbers (quantity) we use must tell us
two things:
 1. How large or small
 2. How well were you able to measure it
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The digits we record in a measurement
(certain and uncertain) are called, significant
figures (sig. figs).
The greater the # of sig. figs in a
measurement, the greater the certainty.

In general, all digits are significant, except
zeros that are not measured but are used to
position the decimal point (place holders).
• Leading zeroes never count as sig. figs
 There are only 3 sig. figs in the quantity 0.00275
kg.
• Internal zeroes always count as sig. figs
 The quantity 1.004 g has 4 sig. figs
• Trailing zeroes count as sig. figs only if the
decimal point is written.
 The quantity 12.40 mL has 4 sig. figs, but the
quantity 250 mL has only 2 sig. figs.
How many sig. figs are in…
12.35 g
Answer
0.00568 L
3 (leading zeroes never count)
3.007 g
4 (internal zeroes always count)
21.0 °C
3 (trailing zeroes count if decimal is
showing)
500 mL
1 (trailing zeroes do NOT count if no
decimal is showing –– but don’t leave
them out, or it looks like 5 mL!)
3 (leading zeroes never count, but trailing
zero counts if decimal is showing)
0.0250 L
4 (count all non-zero digits, not just
decimal places)
Sig. Figs
Sig.
Figs
a. 0.103 cm
i. 2, 300 g
b. 2.306 in
j. 8.10 L
c. 21
k. 2.40603 x 105 µm
d. 0.032 mL
l. 0.000200 kg
e. 1000 mL/L
m. 144
f. 100. Lbs
n. 1001 tons
g. 85 boxes
o. 340. lbs
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Answers to calculation cannot be more
accurate than the information you entered in
calculation- but calculators don’t know that.
2 rules when reporting the uncertainty in
calculations.
 Addition and Subtraction
 Division and Multiplication
When adding or subtracting, round off to the
fewest number of decimal places.
22.9898 g
1.00794 g
12.011 g
47.9982 g
84.00694 g, round to 5 sig. figs 84.007 g
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Keep the same number of sig. figs. as the
measurement with the least number of sig.
figs
Example :
1.2m X 2.00m = 2.4 m
The first measurement 1.2 has 2 sig. figs The
second measurement has 3 sig. figs. So your
answer may only have 2 sig. figs
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1.234g + 2.2g + 3.45g =
2.2m X 333m =
47.0 m  2.2 s =
4.257 kg x (1019 m2 – 40 m2)  (54.5 s x 31.3 s)
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
6.9 g
7.3 X 102 -You have to change the number to scientific
notation because that is the only way you can have two sig.
figs
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21 m/s
2.44 kg·m2/s2
You’ve observed the changes that occur when you
place a piece of Al foil into a blue solution.
 Lots of observations (avoid jumping to
conclusions)
 Bubbles form (gas behaves like H2 gas)
 You’ve observed the relationship between P and V
 Best to quantify observations (measured volumes
while applying pressure)
 PV = constant (1662 Robert Boyle- Boyle’s Law)
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Boyle’s Law describes what gases do, but not
why. To answer the “why” we need a model.
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Imagine air as a collection of particles (tinyping pong balls) bouncing around inside
syringe.
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Tiny particles = molecules
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Every time a molecule hits the syringe wall or
plunger, it pushes against surface.
 The surface pushes back and molecule bounces
off in another direction.
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This process is called gas pressure.
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Now, let’s say we decrease the volume of the
syringe. What happens to the molecules
inside the syringe ? They move!
 Smaller volume = more collisions = more gas
pressure
 This moving-particles model of gases is called the
kinetic molecular theory of gases.
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You bet!
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Here are some examples:
 Inflating a bike tire
 Inflating a balloon
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All gases obey Boyle’s Law and KMT of gases
seems to explain gas pressure behavior for all
gases.
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Absolutely not! Think gas splint test.
 Example: CO2 extinguishes flame
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Different gases= different molecules
(particles are always moving and bouncing
around, PV relationship is the same)
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Now, the question is what happens when
different kinds of gases are combined?