Transcript Sig figs, stats and density

Using Scientific Measurements
Chapter 2
Section 3
Objectives
 Distinguish between accuracy and precision
 Determine the number of significant figures
 Perform mathematical operations involving significant
figures
 Convert measurements into scientific notation
 Distinguish between inversely and directly proportional
relationships
Accuracy and Precision
(i) Accuracy: refers to how close an answer is to the “true”
value

Generally, don’t know “true” value

Accuracy is related to systematic error
(ii) Precision: refers to how the results of a single
measurement compares from one trial to the next

Reproducibility

Precision is related to random error
Low accuracy, low precision
High accuracy, low precision
Low accuracy, high precision
High accuracy, high precision
Significant Figures
• Non-zero numbers are always significant.
For example, 352 g has 3 significant figures.
• Zeros between non-zero numbers are always significant.
For example, 4023 mL has 4 significant figures.
• Zeros before the first non-zero digit are not significant.
For example, 0.000206 L has 3 significant figures.
• Zeros at the end of the number after a decimal place are
significant.
For example, 2.200 g has 4 significant figures.
• Zeros at the end of a number before a decimal place are
ambiguous (e.g. 10,300 g).
Multiplying & Dividing
Least # of sig figs in value
Example:
4.870
x 3.21
15.6
Adding & Subtracting
Least precise number--usually determined by Least # of
decimal places
Examples:
2.345
2500.
+ 0.1__ + 27.3
2.4
2527.
Rounding Rules
If the first digit to be removed is 5 or greater, round UP, 4
or lower, round DOWN.
Example: 2.453 rounded to
2 sig figs is 2.5
5.532 rounded to 3 sig figs
is 5.53
Percent Error
 Percent Error:
 Measures the accuracy of an experiment
 Can have + or – value
accepted  experimeta l
100%
accepted
Example
 Measured density from lab experiment is 1.40 g/mL.
The correct density is 1.36 g/mL.
 Find the percent error.
1.36 - 1.40
% error 
100  2.94%
1.36
Density
Used to characterize substances (a measure of
“compactness”) and is an intensive property.
Defined as mass divided by volume:
mass
Density 
volume
Mass and volume are extensive properties,
they are dependant on the amount of substance.
Units: g/cm3. Sometimes this is written as g • cm–3.
NOTE: cm3 = mL
Frequently used as a conversion factor (mass to
volume)
Bromine is one of two elements that is a liquid at room
temperature (mercury is the other). The density of bromine
at room temperature is 3.12 g/mL. What volume of bromine
is required if a chemist needs 36 g for an experiment?
36 g
V
3.12 g / mL
m
V
d
Solution: 11.53 mL
Sig fig
12 mL
Volume from Mass and Density
What volume is occupied by 461 g of
mercury when it’s density is 13.6 g/ mL?
Solution
Here we can express the inverse of density as a
ratio, 1.00 mL/13.6 g, and use it as a conversion
factor.
1 mL
V = 461 g x –––––
= 3.9 mL
13.6 g
A metal ball was found to have a mass of 0.085 kg
and a volume of 3.1 mL. Calculate the density
of the metal ball in units of g/mL.
The density of liquid mercury is 13.55 g/cm3. A
mercury thermometer contains exactly 0.800 mL
of liquid mercury. Calculate the mass of the
liquid mercury contained in the thermometer.
A glass container weighs 48.462 g. A sample of
4.00 mL of antifreeze solution is added, and
the container plus the antifreeze weigh 54.51 g.
Calculate the density of the antifreeze solution.