**1. **Significant Figures and Scientific Notation

**2. **Significant Figures When using our calculators we must determine the correct answer; our calculators are mindless drones and don?t know the correct answer.
There are 2 different types of numbers
Exact
Measured
Measured number = they are measured with a measuring device so these numbers have ERROR.
When you use your calculator your answer can only be as accurate as your worst measurement

**3. **Exact Numbers An exact number is obtained when you count objects or use a defined relationship.

**4. **Learning Check Classify each of the following as an exact or a
measured number.
1 yard = 3 feet
The diameter of a red blood cell is 6 x 10-4 cm.
There are 6 hats on the shelf.
Gold melts at 1064?C.

**5. **Classify each of the following as an exact (1) or a
measured(2) number.
This is a defined relationship.
A measuring tool is used to determine length.
The number of hats is obtained by counting.
A measuring tool is required.
Solution

**6. **Measurement and Significant Figures Every experimental measurement has a degree of uncertainty.
The volume at right is certain in the 10?s place, 10mL<V<20mL
The 1?s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place.

**7. **What is the Length? We can see the markings between 1.6-1.7cm
We must guess between .6 & .7
We record 1.67 cm as our measurement

**8. **Learning Check

**10. **Note the 4 rules When reading a measured value, all nonzero digits should be counted as significant.
There is a set of rules for determining if a zero in a measurement is significant or not.
RULE 1. Zeros in the middle of a number are like any other digit; they are always significant. Thus, 94.072 g has five significant figures.
RULE 2. Zeros at the beginning of a number are not significant; they act only to locate the decimal point. Thus, 0.0834 cm has three significant figures, and 0.029 07 mL has four.

**11. **RULE 3. Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant. 138.200 m has six significant figures. If the value were known to only four significant figures, we would write 138.2 m.
RULE 4. Zeros at the end of a number and before an implied decimal point may or may not be significant. We cannot tell whether they are part of the measurement or whether they act only to locate the unwritten but implied decimal point.

**12. ** Practice

**13. **Examples of Rounding For example you want a 4 Sig Fig number

**14. **Practice Rule #2 Rounding Make the following into a 3 Sig Fig number

**15. **RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers.

**16. **Chapter Two Multiplication and division

**17. **RULE 2. In carrying out an addition or subtraction, the answer cannot have more significant digits BEFORE or AFTER the DECIMAL point than either of the original numbers.

**18. **Addition/Subtraction 25.5 32.72 320
+34.270 - 0.0049 + 12.5
59.770 32.7151 332.5
59.8 32.72 330

**19. **Addition and Subtraction

**20. **Chapter Two Mixed Order of Operation

**21. **How wide is our universe? 210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

**22. **Scientific Notation A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

**23. **Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1

**24. **2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal?
23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023

**25. **Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places?
8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8

**26. **Write 28750.9 in scientific notation. A. 2.87509 x 10-5
B. 2.87509 x 10-4
C. 2.87509 x 104
D. 2.87509 x 105

**27. **Express 1.8 x 10-4 in decimal notation. 0.00018
Express 4.58 x 106 in decimal notation.
4,580,000
On the calculator, scientific notation is done with the button.
4.58 x 106 is typed 4.58 6

**28. **Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2 Type 4.5 -5 1.6 -2
You must include parentheses if you don?t use those buttons!!
(4.5 x 10 -5) (1.6 x 10 -2)
0.0028125
Write in scientific notation.
2.8 x 10-3

**29. **Use a calculator to evaluate: 7.2 x 10-9 1.2 x 102On the calculator, the answer is: 6.E -11
The answer in scientific notation is
6.0 x 10 -11
The answer in decimal notation is
0.000000000060

**30. **Write (2.8 x 103)(5.1 x 10-7) in scientific notation. A. 14.28 x 10-4
B. 1.4 x 10-3
C. 14.28 x 1010
D. 1.428 x 10-3

**31. **Write in PROPER scientific notation.(Notice the number is not between 1 and 10) 234.6 x 109 2.346 x 1011
0.0642 x 104
6.42 x 10 2

**32. **Write 531.42 x 105 in scientific notation. .53142 x 102
5.3142 x 103
C. 53.142 x 104
D. 531.42 x 105
E. 53.142 x 106
F. 5.3142 x 107
G. .53142 x 108