L07 Chem 111A Study Guide - Fall 2018, Comprehensive Midterm Notes - Wavelength, Wave Function, Integer

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12 Oct 2018
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L07 Chem 111A
MIDTERM EXAM
STUDY GUIDE
Fall 2018
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Chem 111A Fall 2017
Significant Figures and Rounding
Significant figures are the digits used to represent the precision of a measured or
calculated quantity. Below is a summary of the rules for significant figures, which will
be used in Chem 111A. For additional information, please read pages A.5-A.7 in the
back of your textbook (Oxtoby, Gillis & Campion, 7th edition).
Rules:
1. For addition or subtraction, the answer should contain the same number of
decimal places as the term with the fewest decimal places.
Example:
161.032
5.6 Number with fewest digits after the decimal
+ 32.4524
199.0844 199.1 (1 digit to the right of the decimal)
2. For multiplication or division, the answer should contain no more significant
figures than the term with the fewest significant figures.
Example:
152.06 x 0.24 = 36.49  36 (2 significant digits)
3. In multi-step calculations, you may round at each step or round at the end only.
4. Exact numbers, such as integers, are treated as if they had infinitely many
significant figures.
5. Round 5’s to the nearest even number when all the subsequent digits are zero. If
the 5 is followed by one or more non-zero digits, round up.
1. Significant figures
How many significant figures are there in the following numbers?
a. 12.3456
Answer: 6 significant figures (All the digits are significant.)
b. 0.005030
Answer: 4 significant figures (The zeros preceding the first nonzero digit are
place holders and are used to locate the decimal place.)
c. 6000
Answer: Confusing. This number can be counted as having 1 significant figure
or 4 significant figures. A better way to express this number is in scientific
notation; e.g., 6.000 x 103 has 4 significant figures, and 6 x 103 has 1 significant
Contains fewest number
of significant figures
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figure. Note: In Chem 111A, we will make this example clear on exams and
quizzes by using scientific notation.
2. The difference between significant figures and decimal places
Addition
5.05 10-3 + 1.008734
5.05 10-3 has 3 significant figures but if you write it out (0.00505) it has 5
decimal places. This could affect how many places you are allowed to report in
your answer.
1.008734
+ 0.00505
1.013784
We are allowed to report only to the 5th decimal place so the correct answer is
1.01378
Multiplication
(5.05 10-3) (1.008734) = 0.005094107
Since we are doing multiplication, we use the number with the least number of
significant figures, so the correct answer is 0.00509 or 5.09 10-3
3. The correct method of rounding for addition:
Carry out arithmetical operations and THEN round the final answer to the correct
# of significant figures instead of rounding the input data first.
Correct: 15 m
incorrect:
15 m

+ 6.6 m
6.6 m

+ 12.6 m
12.6 m

34.2 
34 m
4. Rounding
Rounding is the procedure of dropping non-significant digits in a calculation
result and adjusting the last digit reported. Look at the leftmost digit to be
dropped:
1. If digit is greater than 5, add 1 to the last digit to be retained and drop all
the digits farther to the right. Thus, rounding 1.2161 to 3 significant
figures gives 1.22
2. If this digit is less than 5, simply drop it and all digits farther to the right.
Rounding 1.2143 to 3 significant figures gives 1.21
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Document Summary

Significant figures are the digits used to represent the precision of a measured or calculated quantity. Below is a summary of the rules for significant figures, which will be used in chem 111a. For additional information, please read pages a. 5-a. 7 in the back of your textbook (oxtoby, gillis & campion, 7th edition). Rules: for addition or subtraction, the answer should contain the same number of decimal places as the term with the fewest decimal places. 5. 6 number with fewest digits after the decimal. 199. 0844 199. 1 (1 digit to the right of the decimal: for multiplication or division, the answer should contain no more significant figures than the term with the fewest significant figures. 152. 06 x 0. 24 = 36. 49 36 (2 significant digits) If the 5 is followed by one or more non-zero digits, round up: significant figures. How many significant figures are there in the following numbers: 12. 3456. Answer: 6 significant figures (all the digits are significant. : 0. 005030.