Name ______KEY_____________
Period ___________________
Significant Figures Calculations, Version 5, Hauck, Ligon
Answer all question below based on the tables provided. Refer to the previous significant
figures lesson if necessary.
Group 1 (Multiplication)
1
2
3
4
Multiplication
I
3.1 x 4.5
125 x 3.31
3.66 x 2.0
2.1 x 5.6984
Correct
answer
14
414
7.3
12
Calculator
Answer?
13.95
413.75
7.32
11.96664
Division
II
1
2
3
4
15 / 2
12 / 2.3695
2004 / 2
0.0375/0.50
Correct
answer
8
5.1
1000
7.5e-2
Calculator
Answer?
7.500
5.06436
1002
7.5e-2
Critical Thinking Questions, CTQ
1. Perform the calculations above on your calculator (and write them in the tables) and compare what you get on
your calculator to the correct ones listed above. Discuss the differences if any and write those down.
The calculator had more digits in the answer. The correct answers had the # SF as the least # digits in the
operation.
2. How many significant figures are in each of the correct answers? List them here
1.
Group 1 Multiplication
# SF
Group 2
# SF
Division
1
2
1
1
2
3
2
2
3
2
3
1
4
2
4
2
3. Compare your answers to CTQ 2 with the number of significant figures in the numbers in the problem itself.
Develop a rule or explanation as to why the correct answer given is the way it is? Write your explanation here:
The answer to the operation only contains the least number of SF in the operation
Group 3 (challenging multiplication & division)
1
2
3
4
Operation
Correct Answer
Calculator Answer
15 x 305
15000.0 / 0.0003
1.230 x 103 x 0.0006
(15 x 3.200 x 10-6) / 3
4.6 x 103
5 x 107
0.7
2 x 10-5
4575.000
5
0.738
1.6 e-5
# SF in
answer
2
1
1
1
4. Perform the calculations on your own (place answers in the calculator answer column for Group 3) and
compare your answers to the correct ones. List the #SF in the answer in the last column of the table. Discuss the
differences if any and write those down.
The correct answers do not contain as many digits as the calculator answers. The correct answer has the same #
SF as the number in the operation with the least # SF.
5. Is this still consistent with your explanation from CTQ 3? Explain.
Yes. In both cases the final answers contain only the least # SF from the operation numbers.
Group 4 (addition and subtraction)
1
2
3
4
5
Operation
Correct Answer
Calculator
Answer
# SF in
answer
2+5
2.90 +14.123
35.00 – 2.0
21. 00987 – 0.87
14.9 + 21.0087 + 3
7
17.02
33.0
20.14
39
7
17.023
33
20.13987
38.9087
1
4
2
4
2
6. Perform the calculations on your own and compare your answers to the correct ones. Discuss the differences
if any and write those down.
The correct answers have fewer digits than the calculator answer and are rounded up if the last digit is 5 or more
at the position of rounding.
7. What do you think is the deciding factor in determining how many significant figures the answer must be
reported in for addition and subtraction problems?
The correct answer in addition and subtraction is only correct when it contains the least number of digits past
the decimal.
Now…here’s a wrench to throw into your rule you made in #7…
Problem: 4050 + 24.4 Answer = 4070
Revamp your rule in #7 to include this new type of addition here:
The numbers in the operation are only 3 SF for both numbers, so the answer can only have 3 SF. Original
answer before determining SF would be 4074.4. However, the answer can not have more SF than allowed, so
must be only 3SF.
8. Discuss and explain the difference between multiplication/division & addition/subtraction rules for sig figs
and write a rule here that describes these differences.
Multiplication and Division, the answer can contain the least #SF from the numbers used in the operation.
Addition and Subtraction can only have the correct #SF in answer based on the accuracy of the numbers in the
operation by looking at the #digits past the decimal.
Group 5 (Mixed addition and subtraction with multiplication and Division)
1
Operation
Correct Answer
Calculator
answer
# SF in correct
answer
(2.09 x 9.1) – 12.89
6.1
6.129
2
2
22.94
15.1269 + (2.50 x 3.12500)
3
519
1.002 + 652.10 – (0.269 / 0.00200)
4
33.04
(9.04-8.23+21.954+81.0)/3.1416
5
0.21
0.20675
8.27 (4.987-4.962)
13. How do you think you should report an answer when an operation involves BOTH addition/subtraction and
multiplication/division? Explain.
Use the least accurate number. If adding or subtracting, look at the #digits past the decimal. Also, looking at the
Multiplication and Division, the answer can contain the least #SF from the numbers used in the operation
14. Revise and complete your set of rules that you have developed accordingly, IF they must be amended.
One needs to use both different sets of rules for each operation.
A website with more explanation of Significant figure rules:
http://www.ruf.rice.edu/~kekule/SignificantFigureRules1.pdf
Exercises:
Perform the following operations and report your answers in the correct number of significant
figures.
Answers are reported in such a way that it reflects the reliability of the least precise
operation
1. 34 x 19.770 = 1.7
2. 120 x 0.081 = 1.48e+03
3. 2.300 x 106 / 19 = 1.2 e+05
4. 12.0 + 12.547 = 24.5
5. 0.0090/ 3.0 = 3.0 e-3
6. 9.00 x 0 .0020 = 4.5 e3
7. (0.00089 x 320.3) – 0.190125= 9.494 e-2
8. 3.5000 x 108 / 1.2 x 10-4 = 2.9 e 12
Scientific Notation/Exponential Notation
9. 0.14 x 6.022 x 1023 =8.4 e 22
10. 2.00x 10 -6 / 3.00 x 10-7 = 6.67 e 0
In a series of calculations, carry the extra digits through to the final result then round. If adding
or subtracting the power of 10 must be the same for all numbers.
Rounding: if 5 or higher round up. Do not round your answer until all calculations have been
made.
11. Add the following to 3 sig figs: (5.22 x 10 4) + (3.21 x 10 2) = 5.25 X 104
12. Subtract the following to 3 sig figs: (6.25 x 10 -2) + (5.77 x 10 -3) = 5.67 X 10-2
More Exercises: mixed operations
13. 4.184 x 100.62 x (25.27-24.16) = 467
14. 9.2 x 100.65 / 8.321+ 4.026 = 75