Standards for Measurement
Accuracy & Precision
Precision:
 How closely individual measurements compare
with each other
 The “fineness” of a measurement
Accuracy: how closely individual measurements
compare with the true or accepted value
Accurate or Precise?
What is the temperature
at which water boils?
•Measurements: 95.0°C,
95.1°C, 95.3°C
•True value: 100°C
Precise!
(but not accurate)
Accurate or Precise?
What is the temperature
at which water freezes?
•Measurements: 1.0°C,
1.2°C, -5.0°C
•True value: 0.0°C
Accurate!
(it’s hard to be accurate
without being precise)
Accurate or Precise?
What is the atmospheric
pressure at sea level?
•Measurements: 10.01
atm, 0.25 atm, 234.5 atm
•True value: 1.00 atm
Not Accurate & Not Precise
(don’t quit your day job)
Accurate or Precise?
What is the mass of one
Liter of water?
•Measurements: 1.000
kg, 0.999 kg, 1.002 kg
•True value: 1.000 kg
Accurate & Precise
(it’s time to go pro)
2.2: Significant Figures
Every measurement has some degree of
uncertainty.
Significant figures (“sig figs”): the digits in a
measurement that are reliable (or precise). The
greater the number of sig figs, the more precise
that measurement is.
A more precise instrument will give more sig
figs in its measurements.
Uncertainty examples:
 To measure the time for a pencil to
fall…compare a stopwatch and a wall clock.
 To measure the volume of a liquid…compare a
graduated cylinder and a beaker.
The stopwatch & graduated cylinder are
more precise instruments…so the readings
they produce will have more sig figs.
A graduated cylinder:
41.2 mL (3 sig figs = very precise)
41.0
100 mL Beaker
50
50 mL Graduated
cylinder
A beaker:
40. mL (2 sig figs = not as precise)
When are digits “significant”?
The “Atlantic-Pacific” Rule
“PACIFIC”
Decimal point
is PRESENT.
Count digits
from left side,
starting with
the first
nonzero digit.
PACIFIC
PACIFIC
40603.23 ft2 = 7 sig figs
0.01586 mL = 4 sig figs
When are digits “significant”?
“ATLANTIC”
Decimal point
is ABSENT.
Count digits
from right side,
starting with
the first
nonzero digit.
3 sig figs = 40600 ft2
1 sig fig = 1000 mL
ATLANTIC
ATLANTIC
Examples
 0.00932
Decimal point present → “Pacific” → count digits from
left, starting with first nonzero digit
= 3 sig figs
 4035
Decimal point absent → “Atlantic” → count digits from
right, starting with first nonzero digit
= 4 sig figs
 27510
Decimal point absent → “Atlantic” → count digits from
right, starting with first nonzero digit
= 4 sig figs
2.4: Scientific Notation
 “Writing a number as a power of 10.”
 Why? It makes very large and very small numbers more
manageable to write and use.
 Rule of thumb: Use when number is greater than 100
or smaller than 0.10. Or, you may always use it!
 The number of sig figs are clearly shown in a
measurement.
2.4: Scientific Notation
How important is a change in the power of 10?
Diameter of Earth’s orbit around the sun
≈ 100,000,000,000 m = 1.0*1011 m
Diameter of an atom
≈ 0.0000000001 = 1.0*10-10 m
Writing in scientific notation
1. Move the decimal point in the original number
so that it is located to the right of the first
nonzero digit.
2. Multiply the new number by 10 raised to the
proper power that is equal to the number of
places the decimal moved.
3. If the decimal point moves:

To the left, the power of 10 is positive.

To the right, the power of 10 is negative.
Write the following measurements in scientific
notation, then record the number of sig figs.
1.
2.
3.
4.
5.
789 g
96,875 mL
0.0000133 J
8.915 atm
0.94°C
7.89*102 g
9.6875*104 mL
1.33*10-5 J
8.915 atm
9.4*10-1 °C
3 sig figs
5 sig figs
3 sig figs
4 sig figs
2 sig figs
Requirements for this class:
Write answers using 3 significant
figures
Use scientific notation for all numbers
greater than 1000 and smaller than
0.001
Accuracy or Precision?
When deciding on accuracy, precision, both, or neither….it is
quantitative data (numerical), not qualitative (descriptive)
1)
2)
3)
4)
The recipe calls for 25 chocolate chips per cookie. The
cookies analyzed have 34, 35, and 32 respectively.
The percent NaCl is 99%, 99%, and 98%.
The number of grams of KF required is 0.04 g. The
amounts used were 0.038, 0.039, 0.041, and 0.040.
To win, Henry must earn 500 points. In his three trials,
he earned 400, 480, and 395 points.
Rounding
Look at digit following specified rounding value. If it is 5 or
greater, then round up. If not, truncate (cut off the rest of
the numbers).
Round to the nearest tenth
6.8
 6.7512
6.8
 6.7777
6.7
 6.7499
7.0
 6.9521
Practice Problems
12.
a)
b)
c)
d)
e)
f)
16.
a)
b)
c)
d)
State the abbreviation
for each of the
following units:
milligram
mg
kilogram
kg
meter
m
nm
nanometer
A
angstrom
L
microliter
State the number of
significant figures in
each of the following
numbers:
3
40.0
2
0.081
6
129,042
4
4.090 x 10-3
18. Round each of the
following numbers to
three significant
figures:
a)
8.8726
8.87
b)
21.25
21.3
c)
129.509
d)
1.995 x 106
130. or 1.30 x 102
2.00 x 106
20. Write each of the
following numbers in
exponential (scientific)
notation:
a)
0.0456
4.56 x 10-2
b)
4082.2
4.08 x 103
4.03 x 101
c)
40.30
d)
12,000,000
1.20 x 107