1. Unit: Introduction to Chemistry
Day 4 - Notes
Unit: Introduction to Chemistry
Types of Measurements and Observations, Scientific Notation

2. Measurement: a type of observation
Qualitative measurements: descriptive
Ex: hot, cold, heavy, light, big, blue, furry
Quantitative measurement: observation made with a measuring instrument and includes both a number and a unit
Ex: ruler, balance, thermometer, graduated cylinder, 13.5°C, 25kg, 17L

3. Accuracy: How close a measurement is to the true or accepted value
Ex: Weighing a 50g mass
50.00g – accurate
32.18g – not accurate
49.99g – accurate

4. Precision: How close multiple measurements are to each other
Ex: Take the weight of a 50g mass
Accurate, precise: Accurate, precise:
50.00g g
50.00g g
Not accurate, precise:
32.18g

5. An easy way to remember…
ACcurate = Correct PRecision = Reproducibility

6. The mass of one gold atom is .000 000 000 000 000 000 000 327 grams.
Scientific Notation is used to express very large and very small numbers so that problem solving will be easier.
Examples:
The mass of one gold atom is
grams.
One gram of hydrogen contains
hydrogen atoms.
Scientists can work with very large and very small numbers more easily if the numbers are written in scientific notation.

7. How to Use Scientific Notation
In scientific notation, a number is written as the product of two numbers…..
…..A coefficient and 10 raised to a power.

8. For example: 4.5 x 103 The coefficient is _______. 4.5
The number 4,500 is written in scientific notation as ________________.
4.5 x 103
The coefficient is _______.
4.5
The coefficient must be a number greater than or equal to 1 and smaller than 10.
The power of 10 or exponent in this example is _____. 3
The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

9. Rules to Remember!
If a number is greater than 10, the exponent will be __________ and is equal to the number of places the decimal must be moved to the _____ to write the number in scientific notation.
positive
left

10. Rules to Remember! right
If a number is less than 1, the exponent will be ___________ and is equal to the number of places the decimal must be moved to the _______ to write the number in scientific notation.
negative
right

11. A number will have an exponent of zero if:
….the number is equal to or greater than 1, but less than 10.

12. 1. Move the decimal to the right of the first non-zero number.
To write a number in scientific notation:
1. Move the decimal to the right of the first non-zero number.
2. Count how many places the decimal had to be moved.
3. If the decimal had to be moved to the right, the exponent is negative.
4. If the decimal had to be moved to the left, the exponent is positive.
To emphasize again: The exponent counts how many places you move the decimal to the left or right.

13. Practice Problems PROBLEMS: ANSWERS 1.2 x 10-4 1 x 103 0.00012
Express the following in scientific notation.
PROBLEMS:
1.2 x 10-4
1 x 103
1 x 10-2
1.2 x 101
9.87 x 10-1
5.96 x 102
7.0 x 10-7
1.0 x 106
1.26 x 10-3
9.88 x 1011
8 x 100
ANSWERS
1000
0.01 12
0.987
596
1,000,000
987,653,000,000 8

14. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
4.9 X 102
3.75 X 10-2
5.95 X 10-4
9.46 X 103
3.87 X 101
7.10 X 100
8.2 X 10-5
490
.0375
9460
38.7
7.10

15. Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.
Using Scientific Notation in Multiplication, Division, Addition and Subtraction

16. Rule for Multiplication
When multiplying numbers written in scientific notation…..
….multiply the first factors and add the exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply 3.2 x Add the exponents
Answer: 6.7 x 102

17. Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Rule for Division
Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.
Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Solution: Divide 6.4 by Subtract the exponents 6 - 2
Answer: 3.8 x 104

18. Rule for Addition and Subtraction
To add or subtract numbers written in scientific notation, you must….express them with the same power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)
Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other.
5.8 x 103 = x so 0.58 x x 104 = ?
Answer: x 104

19. MULTIPLY THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN SCIENTIFIC NOTATION.
Problems:
Answers:
1. (6 x 105) (1 x 102)
2. (4 x 106) (2 x 10-5)
3. (3.4 x 106) (1.8 x 103)
4. (8.1 x 10-7) (3.6 x 102)
5. (4.9 x 104) (6 x 10-3)
6. (5 x 10-5) (2 x 10-6)
7. ( ) (101,654,000,000)
8. (10,456,300,950) (9,754,321)
1. 6 x 107
2. 8 x 101
x 109
x 10-4
x 102
6. 1 x 10-10
x 103
x 1017

20. DIVIDE THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN SCIENTIFIC NOTATION.
Problems:
Answers:
1. (6 x 105)  (2 x 104)
2. (8 x 103)  (2 x 10-5)
3. (7.4 x 104)  (1.8 x 103)
4. (8.19 x 10-4)  (1.6 x 102)
5. (4.3 x 103)  (6.1 x 10-3)
6. (8 x 10-5)  (2 x 10-6)
7. ( )  (101,351,000)
8. (12,701,300,950)  (4,754,321)
1. 3 x 101
2. 4 x 108
x 101
x 10-6
x 105
6. 4 x 101
x 10-14
x 103

21. ADD OR SUBTRACT EACH OF THE FOLLOWING NUMBERS
ADD OR SUBTRACT EACH OF THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN SCIENTIFIC NOTATION.
Problems:
Answers:
1. (6 x 104) + (3 x 104)
2. (6 x 10-5) - (3 x 10-5)
3. (1.4 x 105) + (1.4 x 103)
4. (8 x 104) - (1.6 x 102)
5. (4.9 x 105) + (6.1 x 10-3)
6. (8 x 10-5) - (5 x 10-6)
7. ( ) + (0.196,351,000)
8. (12,701,555,950) - (40,754,321)
1. 9 x 104
2. 3 x 10-5
x 105
x 104
x 105
x 10-5
x 10-1
x 1010

22. Unit: Introduction to Chemistry Significant Figure Rules
Day 5-Notes
Unit: Introduction to Chemistry Significant Figure Rules

23. There is uncertainty in all measurements.
The “certain” digits include all numbers read directly off of the measuring device PLUS one extra estimated digit.
Ex: This device is a graduated cylinder. The units are mL. The proper reading should be:
56.0mL (estimated digit)

24. The amount of definite digits depends on the measuring device.
An exact number has no uncertainty, and therefore has an infinite number of significant figures
Example: 25 people, ….
Defined quantities are considered to be exact.
Example: 12 in=1ft, 100cm=1m

25. Rules for Sig Figs!! 1. All non-zero digits are significant
Example: s.f.
– 5 s.f.

26. 2. Leading zeros are never significant (zeros to the left)
Example: s.f.
0.04 – 1 s.f.

27. 3. Captive zeros are always significant (zeros in the middle)
Example: 205 – 3 s.f.
20005 – 5 s.f.

28. 4. Trailing zeros are sometimes significant (zeros at the end)
a) They are significant if the number contains a decimal point
Example: – 4 s.f.
0.450 – 3 s.f.

29. 4. Trailing zeros (cont.)
b) They are not sig. if the number does not contain a decimal point
Example: 1550 – 3 s.f.
45000 – 2 s.f.

30. Summary 0.000424000600 (Leading)Never sig. (Trailing) (Captive)
Always sig.
(Trailing)
Sometimes sig.
(decimal=sig.)

31. Practice makes perfect!
How many sig figs are in the following?
4.59
3.00
200,202
0.0050
43,000
1.09 x 104 3 3 6 2 2 3

32. Unit: Introduction to Chemistry Significant Figures in Calculations
Day 6- Notes
Unit: Introduction to Chemistry Significant Figures in Calculations

33. Review of yesterday… How many sig figs are in the following? 0.02
0.020
20,020
20,000
2.0x10-3
2,002  1   2     4  1   2     4

34. Sig Figs in Calculations
Addition and Subtraction:
LOOK at the decimal places!
The answer is rounded to the same number of decimal places as the number used in the calculation with the least decimal places.
Ex:
–1.345
7.81~ ~
7.8
5.78

35. Multiplication and Division: LOOK at the total number of sig figs
Multiplication and Division: LOOK at the total number of sig figs! The answer is rounded to the same number of sig. figs. as the number used in the calculation with the least significant figures Ex: 17.85/2.13 = ~ x ~
8.38
0.0017