Name ___________________
Period ___________________
Significant Figures Calculations, Version 5 Hauck and 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 Calculator
answer Answer?
14
414
7.3
12
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?
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.
2. How many significant figures are in each of the correct answers? List them here
1.
Group I
Group II
Multiplication
Division
1
1
2
2
3
3
4
4
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:
Group 3 (challenging multiplication & division)
Operation
Calculator Answer
Correct Answer
1
15 x 305
4.6 x 103
2
15000.0 / 0.0003
5 x 107
3
1.230 x 103 x 0.0006
0.7
4
(15 x 3.200 x 10-6) / 3
2 x 10-5
# SF in
correct
answer
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.
5. Is this still consistent with your explanation from CTQ 3? Explain.
Group 4 (addition and subtraction)
Operation
Calculator
answer
Correct
Answer
1
2+5
7
2
2.90 +14.123
17.02
3
35.00 – 2.0
33.0
4
21. 00987 – 0.87
20.14
5
14.9 + 21.0087 + 3
39
# SF in
correct
answer
6. Perform the calculations on your own and compare your answers to the correct ones. Discuss the
differences if any and write those down.
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?
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:
8. Discuss and explain the difference between multiplication/division & addition/subtraction rules for
sig figs and write a rule here that describes these differences.
Group 5 (Mixed addition and subtraction with multiplication and Division)
1
Operation
Calculator answer Correct
Answer
(2.09 x 9.1) – 12.89
6.129
2
6.1
# SF in
correct
answer
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
8.27 (4.987-4.962)
9. How do you think you should report an answer when an operation involves BOTH
addition/subtraction and multiplication/division? Explain.
10. Revise and complete your set of rules that you have developed accordingly, IF they must be
amended.
Exercises:
Perform the following operations and report your answers in the correct number of
significant figures.
1. 34 x 19.770 =
2. 120 x 0.081 =
3. 2.300 x 106 / 19 =
4. 12.0 + 12.547 =
5. 0.0090/ 3.0 =
6. 9.00 x .0020 =
7. (0.00089 x 320.3) – 0.190125 =
8. 3.5000 x 108 / 1.2 x 10-4 =
Scientific Notation/Exponential Notation
9. 0.14 x 6.022 x 1023 =
10. 2.00x 10 -6 / 3.00 x 10-7 =
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) =
12. Subtract the following to 3 sig figs: (6.25 x 10 -2) + (5.77 x 10 -3) =
More Exercises: mixed operations
13. 4.184 x 100.62 x (25.27-24.16) =
14. 9.2 x 100.65 / 8.321+ 4.026 =
A website with more explanation of Significant figure rules:
http://www.ruf.rice.edu/~kekule/SignificantFigureRules1.pdf