1. Ch. 2 Notes Day 1
Metric Ladder

2. Objectives
SWBAT convert between different metric units using the ladder method
SWBAT identify questions that cannot be converted because suffixes don’t match.

3. Aim: What is the metric system, and why do we use it?
Do Now: On your paper
30ºC = 86 ºF
35 km = 21 miles
Notes are in Yellow.

4. What Type of Measurement do we Normally Use in the USA?
The “English System”
Why don’t we use this system in science?
Too complicated, no logic

5. How Complicated Is It? 12 inches in a foot 3 feet in a yard
16 ½ feet in a rod
120 feet in a furlong
2 pints in a quart
4 quarts in gallon
2 gallons in a peck
4 pecks in a bushel

6. WTFudge? There is no logic so you can’t guess the relationship.
If you want to use the English System, you have to memorize the relationships and multiply or divide to do conversions
Luckily, the metric system is MUCH easier!!!

7. How is the Metric System Easier?
In the metric system, everything is based on units of 10.
Every type of measurement uses the same beginning prefixes.
We can do conversions WITHOUT doing math, just by moving the decimal point right or left.

8. What is the Basic Unit for Length?
Meter abbreviated as m
How long is a meter?
A meter is about a yard. (39.37 inches - a yard is 36 inches)

9. What is the Basic Unit for Volume?
Liter abbreviated as L
How much is a liter?
A liter is about a quart.
(1.06 quarts)

10. What is the Basic Unit for Mass/Weight?
Gram abbreviated as g
How much is a gram?
A gram is very light –
about the weight of a
paperclip! (0.035 ounces)

11. Using the Metric System
Would a meter stick be good enough unit to measure a hair?
No, it’s too big
If you wanted to measure the distance from the earth to the sun, would a meter stick be a good way to measure the distance?
No, it’s too shorteed smaller and larger units

12. Use Prefixes to Make Units Bigger or Smaller
Centi – what does this mean?
1/100 or makes unit smaller
Milli – what does this mean?
1/1000 or makes unit smaller
Kilo – what does this mean?
makes unit larger

13. Conversions are EASY! Let’s Practice!
0.009
A) g = _____ kg
B) L = _____ mL
C) m = _____ cm
0 0 0 .
0 0 0

14. Conversions are EASY! Let’s Practice!
0.009
A) g = _____ kg
B) L = _____ mL
C) m = _____ cm
0.0 0
0 0 0
0 0 0 .
3000
0 0 0 .

15. Conversions are EASY! Let’s Practice!
0.009
A) g = _____ kg
B) L = _____ mL
C) m = _____ cm
0.0 0
0 0 0
0 0 0 .
3000
0 0 0
0 0 0 .
0 0 0 .
500

16. Metric Ladder Review

17. Scientific Notation (106) (103) (102) (101) (100) (10-1) (10-2) (10-3)
(105)
(104)
(103)
(102)
(101)
(100)
(10-1)
(10-2)
(10-3)
(10-4)
(10-5)
(10-6)

18. Ch. 2 Notes Day 2
Scientific Notation

19. Objectives
SWBAT convert long form numbers into scientific notation

20. A short-hand way of writing large numbers without
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.

21. The Distance From the Sun to the Earth
93,000,000 miles

22. Move the decimal so there is only one number in front of it.
Step 1
Move the decimal so there is only one number in front of it.
93,000,000. =

23. Step 2
Write number without zeros
= 9.3

24. Step 3
Count how many places you moved the decimal. Multiply your number by 10.
Take 10 to a power equal to the number of places you moved.
If you moved left, the power is POSITIVE.
If you moved right, the power is NEGATIVE.
93,000,000 = 9.3 x 10 7

25. The power of ten is 7 because the decimal moved 7 places.
93,000,000 = 9.3 x 10 7

26. 93,000, Standard Form
9.3 x Scientific Notation

27. Practice Problem
Write in scientific notation.
Decide the power of ten.
9.85 x 107
98,500,000 = 9.85 x 10?
64,100,000,000 = 6.41 x 10?
279,000,000 = 2.79 x 10?
4,200,000 = 4.2 x 10?
6.41 x 1010
2.79 x 108
4.2 x 106

28. More Practice Problems
On these, decide where the decimal will be moved.
734,000,000 = ______ x 108
870,000,000,000 = ______x 1011
90,000,000,000 = _____ x 1010
Answers
3) 9 x 1010
7.34 x 108
2) 8.7 x 1011

29. Complete Practice Problems
Write in scientific notation.
50,000
7,200,000
802,000,000,000
Answers
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011

30. Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
move the decimal
--->
340,000 in standard form

31. Move the decimal to the right.
Write in Standard Form
Move the decimal to the right.
6.27 x 106
9.01 x 104
6,270,000
90,100

32. Scientific Notation in the Negative
STEP ONE
Move decimal Right
Leave only one number in front of decimal =
STEP TWO
Write number without zeros
7.6

33. Scientific Notation in the Negative
Count how many places you moved decimal
Make that your power of ten
7.6 x10-4
The negative exponent indicates that your standard notation is smaller than 1

34. Ch. 2 Notes Day 3
Significant Figures

35. Objectives Define accuracy Define precision
Compare accuracy & precision
Use significant figures

36. Accuracy
Accuracy refers to how closely a measurement matches the true or actual values
To be accurate only requires the true value (bulls eye) & one measurement (for the arrow to hit the target)
Highly accurate data can be costly and difficult to acquire

37. Precision
Precision refers to the reproducibility of the measurement and exactness of description in a number.
To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

38. Accuracy & Precision
In order to be accurate and precise, one must pay close attention to detail to receive the same results every time as well as “hit the target”.

39. Comparing Accuracy & Precision
Notice the difference in these pictures.
To win the tournament the archers must hit the target the most times. The winner must show accuracy & precision.
The 1st archer has _____ accuracy & ____ precision.
The 2nd archer has _____ accuracy & ____ precision.
The 3rd archer has _____ accuracy & ____ precision.
The 4th archer has _____ accuracy & _____ precision
BAD
BAD
BAD
GOOD
GOOD
GOOD
GOOD
BAD

40. Example 1
A sample is known to weigh g. Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate?
3.200 g
3.180 g
3.152 g
3.189 g

41. Example 2
Consider the data (in cm) for the length of an object as measured by three students. The length is known to be cm. Which student had the most precise work, and which student had the most accurate work?
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Student A
14.8
14.7
Student B
14.2
14.6
Student C
14.4
14.5

42. Solution Most precise: Student A (0.1 cm difference)
Most accurate: Student C (2 were true value, rest within 0.1 cm)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Student A
14.8
14.7
Student B
14.2
14.6
Student C
14.4
14.5

44. Significant Figures Why are significant figures necessary?
True accuracy is no better than the measurement obtained by the least precise method.
We use significant digits so we are not exaggerating our precision.

45. What is a significant figure?
There are 2 kinds of numbers:
Exact: the amount of money in your account. Known with certainty.

46. What is a significant figure?
Approximate: weight, height—anything MEASURED. No measurement is perfect.

47. When to use Significant figures
When a measurement is recorded only those digits that are dependable are written down.

48. Rules of Significant Digits
All digits 1 through 9 are significant.
9.342 mg = 4 Sig. Digits
233,124 = 6 sig. digits

49. Rules of Significant Digits
2. Zero is significant when it is between two non‐zero digits
= 3 SD
206 = 3 SD
100,001 = 6 SD

50. Rules of Significant Digits
3. A zero to the right of a decimal point in a number greater than or equal to one is significant.
(4 SD)
(4 SD)
(4 SD)
(6 SD)
(3 SD)

51. Rules of Significant Digits
4. A zero to the right of a decimal point (in a number less than one) but to the left of nonzero digit is not significant.
(4 SD)
(5 SD)

52. Rules of Significant Digits
5. Zeros used only to space the decimal point (placeholders) are not significant (1 SD) (3 SD) -78,000 (2 SD)

53. Counting SDs How many significant digits are in the following numbers?
1235
2020
235.0
0.0270
235.
65,100
19,620,000,000
102,800

54. Estimated to the tens place Estimated to the tenths place
Why are S.F.s Important?
When reporting a measurement the number of digits indicates the precision of an instrument.
100 ml
Estimated to the tens place
99.9 mL
Estimated to the tenths place

55. Why are S.F.s Necessary?
When you divide 5.0 /0.87 = …
(Actual Answer: 5.7)
S.F.s will provide a way to determine how many numbers to report in a measurement or calcualtion!

56. Example 1:
How would you record this measurement?
1.37 cm

57. Example 2: Provide the measurements for each example.B.

58. How many significant digits would be recorded?10 20 30 40 50 60 70 B. 10 20 30 40 50 60 70 C. 10 20 30 40 50 60 70

59. How many significant digits would be recorded?
48 cm (2 sfs) A. 10 20 30 40 50 60 70 B.
48 cm (2 sfs) 10 20 30 40 50 60 70 C.
48.0 cm (3 sfs) 10 20 30 40 50 60 70