1. #4 Notes : METRIC AND MEASUREMENTS/ Basic Math Tools
Scientific Notation
Significant Digits
Metric System
Dimensional Analysis

2. FOCUSED LEARNING TARGET
In Analyzing data, I will be able to define, explain, interpret the observed measurements through the exploration of Science and Engineering Practices such as the use of :
Scientific Notation
Significant Figures
Rules of Rounding off of Numbers
Measurements
Dimensional Analysis

3. SCIENTIFIC NOTATION 1  x < 10 x 10 exponent
Makes very large or small numbers easy to use
Two parts:
1  x < 10
(including 1 but NOT 10)
x exponent

4. WRITING SCIENTIFIC NOTATION
EXAMPLES:
1) 2,000,000,000
= 2 X 10 9
2) 5430
= X 10 3 3)
= X 10 -7 4)
= X 10 -3
5) 966,666,000
= X 10 8 6)
= X 10 -5
LARGE NUMBERS (>1)
POSITIVE EXPONENTS
EQUAL TO 1 or itself
ZERO EXPONENTS
SMALL NUMBERS (<1)
NEGATIVE EXPONENTS

5. WRITING STANDARD FORM POSITIVE EXPONENTS MOVE TO RIGHT MOVE TO LEFT
EXAMPLES:
1) 4.32 X 10 7
= 43,200,000
2) X 10 3 =
3) 8.45 X 10 -5 =
4) X 10 -9 =
5) 7.00 X 10 -1 =
6) X 10 5
= 112,300
POSITIVE EXPONENTS
MOVE TO RIGHT
MOVE TO LEFT
NEGATIVE EXPONENTS

6. SIGNIFICANT DIGITS Exact numbers are without uncertainty and error
Measured numbers are measured using instruments and have some degree of uncertainty and error
Degree of accuracy of measured quantity depends on the measuring instrument

7. RULES 1) All NONZERO digits are significant
Examples:
a) 543,454,545
= 9
b) 34,000,000
= 2
= 5
c) 65,945
2) Trailing zeros are NOT significant
Examples:
= 1
a) 1,000
b) 234,500
= 4
c) 34,288,900,000
= 6

8. RULES CON’T are significant
3) Zero’s surrounded by significant digits
are significant
Examples:
a) 1,000,330,134
= 10
b) 534,001,000
= 6
c) 7,001,000,100
= 8
4) For scientific notations, all the digits in
the first part are significant
Examples:
a) x 10 9
= 4
b) 2.34 x
= 3
c) x 10 23
= 5

9. RULES CON’T 5) Zero’s are significant if
a) there is a decimal present (anywhere)
b) AND a significant digit in front of the zero
Zero’s at beginning of a number are not significant (placement holder)
Examples: a)
= 3 e)
= 1 f)
= 4 b)
= 7 c)
= 6 g)
= 3 d)
= 9 h)
= 5

10. Rules for Rounding in Calculations

11. Rounding with 5’s: UP ____ 5 greater than zero 10.257 = 10.3 34.3591
= 34.4
ODD zero
99.750
= 99.8
101.15 =

12. Rounding with 5’s:
DOWN
EVEN zero
6.850
= 6.8 =
101.25

13. CALCULATIONS Multiply and Divide: Least number of significant digits
Examples:
a) x x 273 =
b) x 0.14 x x 10 12
= x1010
c) / 44.02 =
d) x x
0.995 =
= 37.5
e) 150 / 4
f) 4.0 x 104 x x 10–3 x x 102 =
g) 3.00 x / x 10 -7
= 7.5 x 1012

14. CALCULATIONS 2) Add and Subtract: Least precise decimal position
Examples: a)
212.2
26.7
402.09
640.99
212.2
26.7
402.09
640.99
212.2
26.7
402.09
640.99
212.2
26.7
402.09
640.99 =

15. ADD AND SUBTRACT CON’T Examples: b) 1.0028 + 0.221 + 0.10337 1.0028
1.0028
0.221
1.0028
0.221
1.0028
0.221 =

16. ADD AND SUBTRACT CON’T Examples: c) 102.01 + 0.0023 + 0.15 102.01
102.01
0.0023
0.15
102.01
0.0023
0.15
102.01
0.0023
0.15 =

17. ADD AND SUBTRACT CON’T Examples: d) 1.000 x 104 - 1 10000 - 1 9999
9999
10000
9999
10000
9999
= x 104

18. ADD AND SUBTRACT CON’T Examples: e) 55.0001 + 0.0002 + 0.104 55.0001
0.0002
0.104
0.0002
0.104 =

19. ADD AND SUBTRACT CON’T Examples:
f) 1.02 x x x 101
1020
102
10.2
1132.2
1020
102
10.2
1132.2
1020
102
10.2
1132.2
1020
102
10.2
1132.2
= 1130

20. MIX PRACTICE Examples: a) 52.331 + 26.01 - 0.9981 = 77.3429 = 77.34=
= 77.34 b)
7.001 =
= 2.04
c) 1.42 x x 103
3.1 x 10 -1 =
= 3.8 x 102
d) ( x 10-4) 2
= x 10-7
= x 10-7
e) ( ) x 4.0 x 103
= 9480
= 9500

21. Why the Metric System? International unit of measurement: SI units
Base units
Derived units
Based on units of 10’s

22. LENGTH Measure distances or dimensions in space Meter (m)
Length traveled by light in a vacuum in 1/ seconds.

23. MASS Measure of quantity of matter Kilogram (kg)
Mass of a prototype platinum-iridium cylinder

24. TIME Forward flow of events Second (s)
Time is the radiation frequency of the cesium-133 atom.

25. VOLUME Amount of space an object occupies Cubic meter (m3)
Derived unit
1 mL = 1 cm3

26. METRIC PREFIXES PREFIX SYMBOL DEFINITION MEGA- M 106 = 1,000,000 KILO-
103 = 1000
HECTO- h
102 = 100
DECA- da
101 = 10
BASE
100 = 1
DECI- d
10-1 = 0.1 = 1/10
CENTI- c
10-2 = 0.01 = 1/100
MILLI- m
10-3 = = 1/1000
MICRO- μ
10-6 = = 1/1,000,000
NANO- n
10-9 = = 1/1,000,000,000

27. DIMENSIONAL ANALYSIS
Process to solve problems
Factor-Label Method
Dimensions of equation may be checked

28. DIMENSIONAL ANALYSIS Examples: 3 years = _______seconds
1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
1 min = 60 seconds
3 years
365 days
24 hours
60 minutes
60 seconds
1 year
1 day
1 hour
1 minute
= seconds
= 9 x seconds

29. DIMENSIONAL ANALYSIS Examples: b) 300.100 mL = ________kL
1 L = 1000 mL
1 kL = 1000 L mL
1 L
1 kL
1000 mL
1000 L
= x 10-4 kL
= x 10 –4 kL

30. DIMENSIONAL ANALYSIS Examples: c) 9.450 x 109 Mg = _________dg
1 Mg = 10 6 g
1 g = 10 dg
9.450 x 109 Mg
10 6 g
10 dg
1 Mg
1 g
= x 1016 dg

31. Experiment 1 : Measure and Convert Using Dimensional Analysis
Lab Station
1: Measure the total width( short side) of the 2 tables
Together
Width =______ centimeter(cm)
Show conversion using dimensional analysis
Width = _______meters (m)

32. Lab Station 2:
Measure the length (long side) of one table
Length = ______ centimeter(cm)
Show your conversion using dimensional analysis
Length = ______meters(m)

33. Lab Station 3:
Measure the mass of the weight using the triple beam balance :
Mass = _________grams(g)
Show your conversion using dimensional analysis
Mass = _______kilograms(Kg)

34. Lab Station 4:
Measure the Mass of the object using the digital scale
Mass = _______ grams (g)
Show your conversion using dimensional analysis
Mass= _________kilogram (kg)

35. Lab Station 5
Measure the Volume of water using
The Graduated cylinder
Volume = _____ milliliter(mL)
Show your conversion using dimensional analysis
Volume = _____ cubic centimeter(cc or cm3)

36. Lab Station 6 :
Measure the volume of soda using the Graduated Cylinder
Volume = ______ milliliter (mL)
Show your conversion using dimensional analysis
Volume = ______ Liter (L)

37. Lab Station 7 :
Measure the dimensions of the block.
Length =____ cm
Width =_____ cm
Height = ____ cm
Calculate the Volume of the Block . Show calculation
Volume = ______ cm3
Show your conversion using dimensional analysis
Volume = ________ cubic meters (m3)

38. Lab Station 8:
Measure the distance using a meterstick.
Distance = ________ centimeter(cm)
Show your conversion using dimensional analysis
Distance = ________ meter(m)
Distance = ________kilometer(km)

39. Lab Station 9:
Measure your walk time in a given distance
Time = _______ seconds (sec)
Show your conversion using dimensional analysis
Time = _____ hour (h)

40. Lab Station 10 :
Calculate your speed :Show your calculations
Speed (v) = distance / time
Speed (v) = ______ meters/sec or m/s
Show your conversion using dimensional analysis
Speed ( v) = ______ kilometers/ hour or km/h

41. Lab Station 11:
Measure the Temperature of Water
Temperature = _____0F
Convert the temperature to
Temperature = _____0C
Temperature = _____ K

42. DIMENSIONAL ANALYSIS Examples:
d) g OH- = __________ molecules OH-
1 mole = 17 g OH-
1 mole = x molecules
2.356 g OH -
1 mole OH -
6.022 x 1023 molecules
17 g OH -
1 mole OH -
= x 1022 molecules
= x molecules

43. DIMENSIONAL ANALYSIS Examples: e) 45.00 km = __________cm
1 km = 1000 m
1 m = 100 cm
45.00 km
1000 m
100 cm
1 km
1 m
= cm
= x cm

44. DIMENSIONAL ANALYSIS Examples: f) 6.7 x 1099 seconds = _______years
1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
1 min = 60 seconds
6.7 x 1099 seconds
1 hours
1 minute
1 day
1 year
60 seconds
60 minutes
24 hours
365 days
= x 1092 years
= 2.1 x years

45. DIMENSIONAL ANALYSIS Examples: g) 1.2400 g He = __________ Liters He
1 mole = 4 g He
1 mole = 22.4 L
g He
1 mole He
22.4 Liters He
4 g He
1 mole He
= Liters He
= Liters He