1. Significant Figures and Scientific Notation

2. 100 mL Graduated Cylinder
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

3. Significant Figures, Rules for Determining Significant Figures
Nonzero digits are always significant.
Zeros between nonzero digits are significant.
3. Zeros in front of nonzero digits are not significant.
4. Zeros both at the end of a number and to the right of a decimal point are significant.
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Copyright © by Holt, Rinehart and Winston. All rights reserved.

4. Significant Figures, continued
Rules for Determining Significant Figures, continued
Zeros both at the end of a number but to the left of a decimal point may not be significant. If a zero has not been measured or estimated, it is not significant. A decimal point placed after zeros indicates that the zeros are significant.
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Copyright © by Holt, Rinehart and Winston. All rights reserved.

5. Significant figures: Rules for zeros
Leading zeros are not significant.
Leading zero
0.421
– three significant figures
Captive zeros are significant.
Captive zero
4012
– four significant figures
Trailing zeros are significant.
Trailing zero
114.20
– five significant figures

6. Significant Figures Counting Sig Figs Count all numbers EXCEPT:
Leading zeros
Trailing zeros without a decimal point -- 2,500
Courtesy Christy Johannesson

7. Counting Sig Fig Examples
Significant Figures
Counting Sig Fig Examples
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
2 sig figs
Courtesy Christy Johannesson

8. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
Calculating with Sig Figs
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = g
4 SF
3 SF
3 SF
324 g
Courtesy Christy Johannesson

9. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL
Calculating with Sig Figs (con’t)
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.
3.75 mL mL
7.85 mL
3.75 mL mL
7.85 mL
224 g
+ 130 g
354 g
→ 7.9 mL
→ 354 g
Courtesy Christy Johannesson

10. Scientific Method

11. Scientific Notation
In science, we often work with very large or very small numbers:
Ex: Speed of Light = 300,000,000 m/s
Avg speed of snail = m/s
So we don’t have to be repetitive and write out the zeroes, we use Scientific Notation
Express numbers as:
1) A number between 1 and 10
2) Power of 10

12. Scientific Notation 300,000,000 = 3.0 x 108 0.00086 = 8.6 x 10-4
The power of 8 tells us that the decimal point is actually 8 places to the right
= 8.6 x 10-4
The power of NEGATIVE 4 tells us that the decimal place is 4 places to the left
Scientific Notation makes very large or very small numbers easier to work with

13. Calculations using Scientific Notation
When multiplying we multiply the actual number and add the exponents
(3.0 x 108 m/s) x (5.0 x 102 s) = 15 x 1010 m = ?
When dividing we divide the actual numbers and subtract the exponents
1.5 x 1011 m = 1.5 x 1011 – 8s = 0.50 x 103 s = ?
3.0 x 108 m/s