View
254
Download
7
Category
Preview:
Citation preview
METRIC AND MEASUREMENTS
Scientific Notation Significant Digits Metric SystemDimensional Analysis
SCIENTIFIC NOTATION
Makes very large or small numbers easy to useTwo parts:
1 x < 10 (including 1 but NOT 10)
x 10 exponent
WRITING SCIENTIFIC NOTATION
EXAMPLES:
1) 2,000,000,000
2) 5430
3) 0.000000123
6) 0.0000600
4) 0.007872
5) 966,666,000
= 2 X 10 9
= 5.43 X 10 3
= 1.23 X 10 -7
= 7.872 X 10 -3
= 6.00 X 10 -5
= 9.66666 X 10 8
LARGE NUMBERS (>1)
POSITIVE EXPONENTSEQUAL TO 1 or itself ZERO EXPONENTS
SMALL NUMBERS (<1)NEGATIVE EXPONENTS
WRITING STANDARD FORMEXAMPLES:
1) 4.32 X 10 7
2) 3.45278 X 10 3
3) 8.45 X 10 -5
6) 1.123 X 10 5
4) 5.0010 X 10 -9
5) 7.00 X 10 -1
= 43,200,000
= 3452.78
= 0.0000845
= 0.0000000050010
= 112,300
= 0.700
POSITIVE EXPONENTS MOVE TO RIGHT
NEGATIVE EXPONENTS MOVE TO LEFT
SIGNIFICANT DIGITS
Exact numbers are without uncertainty and error Measured numbers are measured using instruments and have some degree of uncertainty and errorDegree of accuracy of measured quantity depends on the measuring instrument
RULES1) All NONZERO digits are significant
Examples:
a) 543,454,545
b) 34,000,000
Examples:
c) 65,945
2) Trailing zeros are NOT significant
= 9
= 2= 5
b) 234,500
= 1a) 1,000= 4
c) 34,288,900,000= 6
RULES CON’T3) Zero’s surrounded by significant digits are significant
Examples:a) 1,000,330,134
b) 534,001,000
Examples:
c) 7,001,000,100
4) For scientific notations, all the digits in the first part are significant
= 10
= 6
= 8
b) 2.34 x 10 -
16
= 4a) 1.000 x 10 9
= 3c) 3.4900 x 10 23 = 5
RULES CON’T5) Zero’s are significant if a) there is a decimal present (anywhere) b) AND a significant digit in front of the zeroZero’s at beginning of a number are not significant (placement holder)
Examples:
a) 0.00100
b) 0.1001232
c) 1.00100
= 3
= 7
= 6
e) 0.0000007
= 9d) 8900.00000
= 1
f) 0.003400 = 4
g) 0.0700 = 3
= 5h) 0.040100
Rules for Rounding in Calculations
Rounding with 5’s: UP ____ 5 greater than zero
10.257 = 10.3
34.3591 = 34.4
ODD 5 zero
99.750 = 99.8
101.15 = 101.2
Rounding with 5’s:
DOWN
EVEN 5 zero
6.850 = 6.8
101.25 = 101.2
CALCULATIONS1) Multiply and Divide: Least number of significant digits
Examples:
a) 0.102 x 0.0821 x 273b) 0.1001232 x 0.14 x 6.022 x 10 12c) 0.500 / 44.02
= 2.2861566
= 8.4412 x1010
= 0.011358473
e) 150 / 4
= 2958.770205d) 8900.00000 x 4.031 x 0.08206 0.995 = 37.5
f) 4.0 x 104 x 5.021 x 10–3 x 7.34993 x 102= 147615.9941
g) 3.00 x 10 6 / 4.00 x 10 -7 = 7.5 x 1012
CALCULATIONS2) Add and Subtract: Least precise decimal position
Examples:
a) 212.2 + 26.7 + 402.09
212.2 26.7402.09640.99
212.2 26.7402.09640.99
212.2 26.7402.09640.99
212.2 26.7402.09640.99
= 641.0
ADD AND SUBTRACT CON’T
Examples:
b) 1.0028 + 0.221 + 0.10337
1.00280.2210.103371.32717
1.00280.2210.103371.32717
1.00280.2210.103371.32717
1.00280.2210.103371.32717
= 1.327
ADD AND SUBTRACT CON’T
Examples:
c) 102.01 + 0.0023 + 0.15
102.01 0.0023 0.15102.1623
102.01 0.0023 0.15102.1623
102.01 0.0023 0.15102.1623
102.01 0.0023 0.15102.1623
= 102.16
ADD AND SUBTRACT CON’T
Examples:
d) 1.000 x 104 - 1
10000- 1 9999
10000- 1 9999
10000- 1 9999
= 1.000 x 104
ADD AND SUBTRACT CON’T
Examples:
e) 55.0001 + 0.0002 + 0.104
55.0001 0.0002 0.10455.1043
55.0001 0.0002 0.10455.1043
55.0001 0.0002 0.10455.1043
= 55.104
ADD AND SUBTRACT CON’T
Examples:
f) 1.02 x 103 + 1.02 x 102 + 1.02 x 101
1020 102 10.21132.2
1020 102 10.21132.2
1020 102 10.21132.2
1020 102 10.21132.2
= 1130
MIX PRACTICEExamples:
a) 52.331 + 26.01 - 0.9981 = 77.34= 77.3429b) 2.0944 + 0.0003233 + 12.22
7.001= 2.04466
= 2.04
c) 1.42 x 102 + 1.021 x 103
3.1 x 10 -1
= 3751.613
= 3.8 x 102
d) (6.1982 x 10-4) 2 = 3.841768 x 10-7= 3.8418 x 10-7
e) (2.3232 + 0.2034 - 0.16) x 4.0 x 103
= 9480
= 9500
Why the Metric System?
International unit of measurement: SI units Base units Derived units
Based on units of 10’s
LENGTHMeasure distances or dimensions in spaceMeter (m)Length traveled by light in a vacuum in 1/299792458 seconds.
MASSMeasure of quantity of matterKilogram (kg)Mass of a prototype platinum-iridium cylinder
TIMEForward flow of eventsSecond (s)Time is the radiation frequency of the cesium-133 atom.
VOLUMEAmount of space an object occupiesCubic meter (m3) Derived unit1 mL = 1 cm3
METRIC PREFIXESPREFIX SYMBO
LDEFINITION
MEGA- M 106 = 1,000,000
KILO- k 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 = 0.001 = 1/1000
MICRO- μ 10-6 = 0.000001 = 1/1,000,000
NANO- n 10-9 = 0.000000001 = 1/1,000,000,000
DIMENSIONAL ANALYSIS
Process to solve problemsFactor-Label MethodDimensions of equation may be checked
DIMENSIONAL ANALYSIS
Examples:a) 3 years = _______seconds 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds3 years
1 year
365 days
1 day
24 hours
1 hour
60 minutes 1
minute
60 seconds
= 94608000 seconds
= 9 x 10 7 seconds
DIMENSIONAL ANALYSIS
Examples:b) 300.100 mL = ________kL 1 L = 1000 mL 1 kL = 1000 L 300.100 mL
1000 mL
1 L
1000 L
1 kL
= 3.001 x 10-4 kL = 3.00100 x 10 –4
kL
DIMENSIONAL ANALYSIS
Examples:c) 9.450 x 109 Mg = _________dg 1 Mg = 10 6 g 1 g = 10 dg 9.450 x 109 Mg
1 Mg
10 6 g
1 g
10 dg
= 9.450 x 1016 dg
DIMENSIONAL ANALYSIS
Examples:d) 2.356 g OH- = __________ molecules OH-
1 mole = 17 g OH-
1 mole = 6.022 x 10 23 molecules 2.356 g OH -
17 g OH -
1 mole OH -
1 mole OH -
6.022 x 1023 molecules
= 8.34578 x 1022 molecules = 8.346 x 10 22
molecules
DIMENSIONAL ANALYSIS
Examples:e) 45.00 km = __________cm 1 km = 1000 m 1 m = 100 cm 45.00 km
1 km
1000 m
1 m
100 cm
= 4500000 cm= 4.500 x 10 6 cm
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 seconds6.7 x 1099 seconds
60 seconds
1 minute
60 minutes
1 hours
24 hours
1 day
365 days
1 year
= 2.124556 x 1092 years
= 2.1 x 10 92 years
DIMENSIONAL ANALYSIS
Examples:g) 1.2400 g He = __________ Liters He 1 mole = 4 g He 1 mole = 22.4 L 1.2400 g He
4 g He
1 mole He
1 mole He
22.4 Liters He
= 6.944 Liters He= 6.9440 Liters He
Recommended