Transcript significant figures

The Mathematics of Chemistry
Accuracy and Precision
Certainty vs. Uncertainty
Significant Figures
Accuracy and Precision
• Accuracy refers to how closely a measurement
agrees with the accepted or true value.
• Precision refers to reproducibility of
measurements.
• Chemistry calculations utilize significant figures
to communicate uncertainty.
Accuracy and Precision
#3
• #1
#4
#1
#2
Uncertainty in Measurement
• Measurements always have uncertainty.
• Significant figures are the number of digits
that are certain (can be measured) and the
first uncertain digit.
Rules for Significant Figures:
Non-zero digits
digits and
1.1.Non-zero
andzeros
zerosbetween
betweennonzero digitsdigits
are always
significant.
non-zero
are always
significant.
2.2.Leading
zerosare
arenot
notsignificant.
significant.
Leading zeros
3. Zeros to the right of all non-zero digits
3. Zeros to the right of all non-zero digits are
are only significant if a decimal point
only significant if a decimal pointis shown.
is shown.
Rules for Finding Significant Figures
Rule #1- Non-zero digits and zeros
between non-zero digits are always
significant.
00340.003210
Rules for Finding Significant Figures
Rule #1- Non-zero digits and zeros
between non-zero digits are always
significant.
00340.003210
Rules for Finding Significant Figures
Rule #2 - Zeros to the right of all non-zero
digits are only significant if a decimal point is
shown.
00340.003210
Rules for Finding Significant Figures
These zeros are not significant. There is
not a rule that supports counting them.
00340.003210
How many significant figures?
00340.0
4
Rule #3
How many significant figures?
800.1
4
Rule #1
How many significant figures?
0800.10
5
Rules # 1 and 3
How many significant figures?
800
1
Rule #3
How many significant figures?
800.
3
Rule #3
How many significant figures?
0.008
1
Rule #2
How many significant figures?
0.180
3
Rule # 3
Using Significant Figures when Adding and
Subtracting in Calculations
1. Determine the number of significant figures in
the decimal portion of each of the numbers in
the problem.
2. Add or subtract the numbers.
3. Round the answer to match the least number of
places in the decimal portion of any number in
the problem.
Using Significant Figures when Adding and
Subtracting
Give it a try!
Add 0.03 g of NaCl to 155 g of water. What is
the total mass?
Answer: 155 g because the mass of water has
no decimal places, so the final answer must
be written with no decimal places.
Using Significant Figures when Adding and
Subtracting
892.542g
20.629g
0.18g
+ 4.20g
3
3
2
2
917.551
The least amount of significant figures to the right of the decimal in the numbers
is 2; therefore, the answer should only have 2 significant figures to the right of
the decimal.
917.55 g
Using Significant Figures when Multiplying
and Dividing
• Determine how many significant figures each
numbers being multiplied or divided has, and note
which number has the fewest.
• Complete the calculation.
• Write the answer using the same number of
significant figures as the least number of significant
figures found in the numbers used in the calculation.
Using Significant Figures when Multiplying
and Dividing
28.3 cm X 5.0 cm = ____cm2
28.3 has 3 significant figures, and 5.0 has 2
significant figures; therefore, the answer
141.5 should be written 140, so that it only
has 2 significant figures.
140 cm2
Try it!
454.02 g of aluminum hydroxide multiplied by
5.2 g equals how many grams?
454.02 g X 5.2 g = _____ g
Rule: Write the answer using the same number of
significant figures as the least number of
significant figures found in the numbers used in the
calculation.
Scientific Notation
Expanded Notation
Scientific Notation
A.
B.
C.
D.
A.
B.
C.
D.
0.00263 moles
.000000190 moles
259, 351.6 grams
100,000 milliliters
2.63 X 10- 3 moles
1.90 X 10-7 moles
2.593516 X 105 grams
1 X 105 milliliters