Answer in complete sentences.1. What is the volume in this

graduated cylinder (in mL)?2. What is the uncertainty?3. What could you do to find a more

accurate value for the volume?4. Do you think this graduated

cylinder is accurate? Why or why not?

5. If I read volumes of 8.11, 8.12, and 8.10 mL from this picture, would my answer be accurate, precise, both, or neither? Explain your answer.

• An engineer was responsible for calculating amount of water that overflowed from a dam. He measured all of the water runoff going into the reservoir (1.2 million cubic feet per year), the rainfall (860 cubic feet per year), and the capacity of the reservoir (3.8 million cubic feet). He did some fancy calculations. He reported to his boss that the overflow from the dam would be 350,246.2544330 cubic feet per year.

• What’s wrong here?

Significant Figures and Scientific Notation

I. Significant Figuresaka: Significant Digits

• A. Nonzero integers count as significant figures– Ex. Any number that is NOT zero (1, 2, 3, 4,

5, 6, 7, 8, 9)– 345– 597.2– 145.456

• Zeros– B. Leading zeros that come before all the

nonzero digits do NOT count as significant figures

– Ex: 0.0025 has two sig. fig. The zeros are “leading” and do not count.

– 0.23– 0.0004– 0.03564

– C. Captive zeros are between nonzero digits and DO count as sig. fig.

– Ex: 1.008 has four sig. fig. The zeros are captive and DO count.

– 10,004– 1.000006– 1,000,000,000,000,567

– D. Trailing zeros are to the right end of the number and DO count as sig. fig. if the number contains a decimal point.

– Ex.: 100 has only one sig. fig. because the trailing zeros DO NOT have a decimal point.

– Example: 1.00 has three sig. fig. because the trailing zeros DO have a decimal point.

– 1.000000– 3,000,000– 3.00000– 30.00– 300– 300.

• E. Exact numbers– Any number found by counting has an

infinite number of significant figures.– Ex: I have 3 apples. The 3 has an infinite

number of significant figures.– 50 people– 100 baseballs

Which are exact numbers?

1. The elevation of Breckenridge, Colorado is 9600 feet.

2. There are 12 eggs in a dozen.3. One yard is equal to 0.9144 meters.4. The attendance at a football game was

52,806 people.5. The budget deficit of the US

government in 1990 was $269 billion.6. The beaker held 25.6 mL of water.

Practice – Copy the number and identify the number of significant figures.

1. 256

2. 647.9

3. 647.0

4. 321.00

5. 4005

6. 0.45

7. 0.00045

8. nine

9. 200.

10. 200.0

11. 0.009009

12. -500

13. 100.007

14. -500.0

15. -500.

16. 1.30x1032

How many significant figures?

1. A student’s extraction procedure yields 0.0105 g of caffeine.

2. A chemist records a mass of 0.050080 g in an analysis.

3. In an experiment, a span of time is determined to be 8.050 x 10-3 s.

4. Rewrite 8.050 x 10-3 so it has three significant figures.

• The sample of gold contained 1,200,000,000,000,000,000,000,000,000 atoms.

• How do we keep track of ALL those zeros?

• In chemistry, some numbers are HUGE!

II. Scientific Notation(aka: Exponential Notation)

• 8,000,000 =

• 0.00012 =

• Integer must be 1≤x<10

• Positive exponent: number > 1

• Negative exponent: number < 1 (but > 0!)

• 4,500,000• 3,950,000,000• 230• 230.• 0.00000045• -0.002• 0.00781

Copy the number and rewrite in scientific notation

a. 100,000

b. -5,000,000

c. 450,000,000,000

d. 1,300

e. 0.01

f. 0.00 005

g. -0.0 045

h. 0.00 000 000 000 000 023

Remember…

• A negative exponent is a tiny number but is bigger than 0 (NOT a negative number!)

• A big exponent is a HUGE number.

• A negative number can have either a positive exponent or a negative exponent.

Round to three sig. fig. and express in exponential notation.

1. 745,000

2. 0.00054000

3. 540,321,324

4. 0.143589

Homework

• Handout: Significant Figures and Scientific Notation

III. Rules for Sig. Fig. in Mathematical Operations

• A. Multiplication and Division– The number of sig. fig. in the results should

be the same as the number of sig. fig. in the least precise measurement used in the calculation.

– Example: 4.56 x 1.4 = 6.38 6.4

• B. Addition and Subtraction– The result should have the same number of

decimal places as the least precise measurement used in the calculation.

– Example: 12.11 + 18.0 + 1.013 = 31.123 31.1 (one decimal place)

• 13 x 1.000 = 13.000 =

• 23.45 x 400 = 9380 =

• 5000 / 3.12 = 1602.56410256…

• 14 + 3.567 = 17.567

• 56.2 + 23.988 = 80.188

• 100 – 1.9995 = 98.0005

IV. Rounding

• Calculate first, then round

• Example: round 4.348 to two sig. fig.– 4.3– Never round until your final answer!

Assignment

• P. 32 #8