Transcript Uncertainty in Measurement

Significant Figures
Uncertainty in
Measurement
Because Nothing in physics
is ever certain…
Measurement in Science
Quantitative observations
(measurements) must consist of
two parts: a number and a unit
Mrs. Petraroi is 5 feet 8
inches tall
What would happen if we did not have units??
Measuring Volume in the Lab
Volume is measured
from the bottom of
the meniscus
Uncertainty in Measurement
Any measurement involves
an estimate and thus is
uncertain to some extent
Uncertainty in measurement
If 5 different people took a
measurement of a pin, we could
have 5 different measurements:
Person
1
2
3
4
5
Measurement
2.85 cm
2.84 cm
2.86 cm
2.85 cm
2.86 cm
Uncertainty in measurement
If 5 different people took a
measurement of a pin, we could
have 5 different measurements:
Person
1
2
3
4
5
Measurement
2.85 cm
2.84 cm
2.86 cm
2.85 cm
2.86 cm
The first two digits are the
same regardless of who
made the measurement
(these are called certain
numbers))
Uncertainty in measurement
If 5 different people took a
measurement of a pin, we could
have 5 different measurements:
Person
1
2
3
4
5
Measurement
2.85 cm
2.84 cm
2.86 cm
2.85 cm
2.86 cm
The last digit
varies; it is called
the uncertain
number
You Try…
Take the Volume of the liquids in
the next two graduated
cylinders
1 minute to discuss and write
your answer
1. Uncertainty in Measurement
Take the
Volume!
(Always take a
measurement to the
first uncertain
number.)
1. Uncertainty in Measurement
To be correct,
your answer
must be in the
following
range:
56.0-56.9mL
2. Uncertainty in Measurement
Take the
Volume!
(Always take a
measurement to the
first uncertain
number.)
2. Uncertainty in Measurement
To be correct,
your answer
must be in the
following
range:
8.40-8.49mL
Rules for counting Significant Figures
1. Nonzero numbers always count
Ex: 1457 has 4 sig figs
Rules for counting Significant Figures
1. Nonzero numbers always count
2. Leading zeros never count
Ex: 0.0025 has 2 sig figs
15,677
0.0391
Rules for counting Significant Figures
1. Nonzero numbers always count
2. Leading zeros never count
3. Captive zeros always count
Ex: 1.008 has 4 sig figs
506
0.06002
Rules for counting Significant Figures
1.
2.
3.
4.
Nonzero numbers always count
Leading zeros never count
Captive zeros always count
Trailing zeros only count if the number
contains a decimal point
Ex: 100 has only 1 sig fig
100. has 3 sig figs
0.4700
5,000
Rules for counting Significant Figures
1.
2.
3.
4.
Nonzero numbers always count
Leading zeros never count
Captive zeros always count
Trailing zeros only count if the number
contains a decimal point
5. Exact numbers (have an unlimited
number)
What is an exact number??
Numbers that are determined by counting:
 10 experiments
 8 molecules
Definitions
 1 inch = 2.54 cm
Significant Figures and Rounding
If the digit to be removed:
 A. is less than 5, the preceding digit stays the
same (1.33 1.3)
 B. is equal to or greater than 5, the preceding
digit is increased by 1 (1.36  1.4)