This document discusses the concept of significant figures and how to determine the number of significant figures in measurements and calculations. It defines significant figures as the "important digits" that indicate the precision of a measurement. Rules are provided for determining significant figures depending on leading or trailing zeros and whether the number is read from left to right or right to left. Examples demonstrate applying these rules and how to round final answers in calculations like addition, subtraction, multiplication and division based on the least precise measurement used. The key takeaway is that significant figures convey precision and final answers should not be more precise than the least precise input.

1. Significant Figures
https://serc.carleton.edu/eddie/

2. Learning Objectives
After completing this vignette, a student should be able to:
• Apply the rules of significant figures for a measurement
• Express numerical values with the correct number of significant figures
using a mnemonic device (the "Atlantic Pacific Rule") 2
• Determine the number of significant figures from a given value or
mathematical operation
Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.

3. How tall is Emerson the Giraffe?

4. What if you use a different
ruler to measure Emerson?
Does it make a difference?

5. What are Significant Figures?
1
• The “important digits” of a number
• They tell us about the precision of the
underlying measurement
• Important in the final answer

6. The precision of your
measuring device
impacts how many
significant figures should
be reported.
Ruler 1: 5.50 m
Ruler 2: 5.5 m

7. Leading and Trailing Zeros 1
Leading
Zeros to the left of the first nonzero
digit are not significant
Trailing
If the 1st digit is > 1, then zeros to the
right of the decimal point are significant
If a digit is < 1, then only the zeros at
the end and the zeros in-between non-
zeros are significant
0.000205  3 Sig Figs
60.090  5 Sig Figs
0.04050  4 Sig Figs

8. General Rules 1
• All leading non-zero digits are significant, if
there are no digits after a decimal point.
• Zeros between nonzero digits are significant
• Leading zeros are never significant
• Trailing zeros in the decimal portion are
significant
6500
9004
0.0064
0.03400
Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.

9. How many Sig. Figs are present?
6500 = ?
9004 = ?
0.0064 = ?
0.03400 = ?

10. Here are the answers!
6500 = 2
9004 = 4
0.0064 = 2
0.03400 = 4

11. Atlantic – Pacific Rule 2
Read values from left to right.
All numbers from the first non-
zero are significant
→ 1.270
4 Sig. Figs!
Read values from right to left
All numbers from the first
non-zero are significant
12700 ←
3 Sig. Figs!
For counting significant figures
Pacific
Decimal is Present
Atlantic
Decimal is Absent
Stone, Helen M. Atlantic-Pacific sig figs. Journal of Chemical Education 66.10 (1989):
829. https://www.sas.upenn.edu/~dbalmer/eportfolio/sigfig_article.pdf

12. Decimal Precision: When to round
1st Rule:
Round up the digit that follow if the
first digit in front is less than 5.
17.53 rounds off to 17.5
17.5 = 3 Significant Figures
2nd Rule:
If the digit is equal or greater than
5, the digit is rounded up by 1.
17.55 rounds up to 17.6
17.6 = 3 significant Figures

13. Addition/Subtraction 1
• Wait to round until the end of
the calculation
• Round final answer to match
the number with the fewest
decimal significant figures
10. 1 ← 1 decimal place
+ 7. 43 ← 2 decimal places
17. 53
17.5 ← Final number
3 Sig. Figs
(Rounded to 1 decimal place)
Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.

14. Multiplication/Division 1
• Wait to round until the end of
the calculation
• Round final answer to match
the number with the fewest
decimal significant figures
1.5 ← ? Sig. Figs
4.93 ← ? Sig. Figs
x 6.027 ← ? Sig. Figs
45 ← ? Sig. Figs
Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.

15. Multiplication/Division 1
• Wait to round until the end of
the calculation
• Round final answer to match
the number with the fewest
decimal significant figures
1.5 ← 2 Sig. Figs
4.93 ← 3 Sig. Figs
x 6.027 ← 4 Sig. Figs
44.5697 ← Round
45 ← 2 Sig. Figs
Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.

20. Take Home Messages!
Significant figures are important - they tell us about the precision of the
underlying measurement
Final answer should not be more precise than the least precise
measurement used in the calculation.