Significant Figure Rules
Provided by the Academic Center for Excellence 1 Reviewed April 2008
Significant Figure Rules
You can navigate to specific sections of this handout by clicking the links below.
Determining Number of Significant Figures (Sig Figs): pg. 1
Addition/Subtraction: pg. 2
Multiplication/Division: pg. 2
Conversions: pg. 3
Sample Problems: pg. 4
Determining Number of Significant Figures (Sig Figs)
1) All non-zero integers are significant.
Example 1: 412945 has 6 sig figs.
2) All exact numbers have an unlimited number of sig figs.
Example 2: If you counted the number of people in your class to be exactly 35,
then 35 would have an unlimited number of sig figs.
Example 3: It has been determined that exactly 60 seconds are in a minute, so 60
has an unlimited number of sig figs.
3) Zeros are significant depending on what kind of zeros they are.
a. Zeros that are between non-zero integers are always significant.
Example 4: The zeros in 100045, 600.4545, and 23.04 are all significant because
they are between non-zero integers.
b. Zeros that come before non-zero integers are never significant.
Example 5: The zeros in 098, 0.3, and 0.000000000389 are not significant
because they are all in front of non-zero integers.
c. If the zeros come after non-zero integers and are followed by a decimal
point, the zeros are significant.
Example 6: The zeros in 1000. are significant because they are followed by a
decimal point.
Significant Figure Rules
Provided by the Academic Center for Excellence 2 Reviewed April 2008
d. If the zeros come after non-zero integers but are not followed by a decimal
point, the zeros are not significant.
Example 7: The zeros in 1000 are not significant because they are not followed by
a decimal point.
e. If the zeros come after non-zero integers and come after the decimal point,
they are significant.
Example 8: The zeros in 9.89000 are significant because they come both after
non-zero integers and after the decimal point.
Addition/Subtraction
When adding/subtracting, the answer should have the same number of decimal places
as the limiting term. The limiting term is the number with the least decimal places.
Example 9:
Example 10: 5365.999
– 234.66706
5131.33194
Multiplication/Division
When multiplying/dividing, the answer should have the same number of significant
figures as the limiting term. The limiting term is the number with the least number of
significant figures.
Example 11: 503.29 x 6.177 = 3108.82233 → round → 3109
↑
limiting term has 4 sig figs
Example 12: 1000.1 = 4.11563786 → round → 4.12
243
↑
6
53
.22
.6
14
.311
+
45
.09091
119
.22191
→ round → 119.2 (answer has 1 decimal place)
← limiting term has 1 decimal place
← limiting term has 3 decimal places
→ round → 5131.332 (answer has 3 decimal places)
limiting term has 3 sig figs
Provided by the Academic Center for Excellence 3 Significant Figure Rules
Conversions
When converting a number, the answer should have the same number of significant
figures as the number started with.
Example 13: 52.4 in x 1 ft = 4.366666667 ft → round → 4.37 ft
↑ 12 in
3 sig figs
Provided by the Academic Center for Excellence 4 Significant Figure Rules
Sample Problems
How many significant figures does each of the following contain?
1. 54
2. 45678
3. 4.03
4. 4.00
5. 400
6. 400.
7. 0.041
8. 65000
9. 190909090
10. 0.00010
Which number in each of the additions/subtractions is the limiting term, and how many
decimal places should the answer of each addition/subtraction have?
11. 55.43 + 44.333 + 5.31 + 9.2
12. 890.019 + 890.1234 + 890.88788
13. 69.99999 – 45.44444444
Which number in each of the multiplication/division problems is the limiting term, and
how many sig figs should the answer of each multiplication/division have?
14. 343.4 / 34.337
15. 0.000000003 x 30.03030
Perform the following operations and round using the correct sig fig rule.
16. 17.12 + 30.123
17. 35.010 / 1.23
18. 1000.00 – 62.5
19. 0.1700 x 1700. x 1700
20. 15.05 + 0.0044 + 12.34
Provided by the Academic Center for Excellence 5 Significant Figure Rules
Answers
1. 2
2. 5
3. 3
4. 3
5. 1
6. 3
7. 2
8. 2
9. 8
10. 2
11. 9.2 is the limiting term; 1 decimal place
12. 890.019 is the limiting term; 3 decimal places
13. 69.99999 is the limiting term; 5 decimal places
14. 343.4 is the limiting term; 4 sig figs
15. 0.000000003 is the limiting term; 1 sig fig
16. 47.24
17. 28.5
18. 937.5
19. 490000
20. 27.39
* Information for this handout was obtained from the following sources:
• Zumdahl. Introductory Chemistry: A Foundation. 5
th
Ed. Houghton Mifflin
Company. 2004.
