Transcript The Mathematics of Chemistry Significant Figures

The Mathematics of
Chemistry
Significant Figures
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.
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.
Rules for Significant Figures:
1. Non-zero digits and zeros between
non-zero digits are always significant.
2. Leading zeros are not significant.
3. Zeros to the right of all non-zero digits
are only significant if a decimal point
is shown.
Rules for Significant Figures:
4. For values written in scientific notation, the
digits are only significant if a decimal point
is shown.
5. In a common logarithm, there are as many
digits after the decimal point as there are
significant figures in the original number.
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 nonzero 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