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Corner Brook Regional High School
Measurement and Calculations Significant Digits Scientific Notation Converting between Units Accuracy vs. Precision
Scalar Quantities Distance Calculations Speed Calculations Distance-Time Graph Speed Time Graph
Vector Quantities Displacement Calculations Velocity Calculations Acceleration Calculations Vector Diagrams
Chapter 9
Intro, 9.2, 9.5, 9.6, 9.7, 9.10
Chapter 10
Intro, 10.2, 10.3, 10.4, 10.7
Chapter 11
Intro, 11.1, 11.3, 11.5, 11.7
DEFINITION:
The study of motion, matter, energy, and force.
Branches include:
▪ MECHANICS (motion and forces)
▪ WAVES (sound and light)
▪ ENERGY (potential and kinetic, thermodynamics)
▪ MODERN (quantum physics, nuclear physics)
CERTAINTY
Defined as the number of significant digits plus one uncertain (estimated) digit
The last digit of any number is always UNCERTAIN, as measurement devices allow you to estimate.
EXAMPLE:
▪2.75 m
The “5” is uncertain
TAKE THE FOLLOWING MEASUREMENT and determine the certain digits and the uncertain digit.
ANSWER:_____________________________
1. EXACT VALUES
EXACT VALUES have an INFINITE (∞) NUMBER of
SIGNIFICANT DIGITS.
▪ TWO TYPES:
COUNTED VALUES – directly counted
▪ Ex: 20 students, 3 dogs, 5 fingers
DEFINED VALUES – always true, constant measures
▪ Ex: 60 s/min, 100 cm/m, 1000 m/km
2. ZEROS
ALL NUMBERS in a value are SIGNIFICANT EXCEPT LEADING ZEROS, and TRAILING ZEROS WITH NO DECIMAL.
VALUE NUMBER OF SIG FIGS
600
606
600.0
0.60
0.606
660
3. MULTIPLYING and DIVIDING
WHEN MULTIPLYING(x) and DIVIDING(/), ANSWER has SMALLEST NUMBER of SIGNIFICANT DIGITS.
EXAMPLE:
6.15 x 8.0 =
8.4231 ÷ 2 =
4. ADDING AND SUBTRACTING
WHEN ADDING(+) and SUBTRACTING(-), ANSWER has SMALLEST NUMBER of DECIMAL PLACES.
EXAMPLE:
104.2 + 11 + 0.67 =
5. ROUNDING
When ROUNDING, if the number is 5 or GREATER, ROUND UP.
Remember, round only once!VALUE ROUND to 2 SIG FIGS
61.3 s
12.70 m/s
36.5 km
99.0 m/s2
46.4 min
A convenient way of expressing very large and small numbers.
Expressed as a number between 1 and 10 and multiplied by 10x (x = exponent).
LARGE numbers
▪ exponent is # of spaces to the LEFT
SMALL numbers
▪ NEGATIVE exponent is # of spaces to the RIGHT
ROUND THE FOLLOWING to 2 SIGNIFICANT DIGITS.
VALUE SCIENTIFIC NOTATION
100 m
3500 s
926,000,000,000 h
0.0043 m
0.0000000001246 s
0.1 m/s2
DO THE 2 ATTACHED WORKSHEETS in your handout for homework.
BASE UNIT A unit from which other units may be derived,
including units for the following:▪ Length metres, m
▪ Mass kilogram, kg
▪ Time second, s
▪ Temperature kelvin, K
In science, we use SI BASE UNITS, from the INTERNATIONAL SYSTEM OF UNITS.
DERIVED UNIT A unit which is derived from base units.
Ex: m/s
METRIC PREFIXES
Values placed in front of the base units.
PREFIX SYMBOL FACTOR
giga G 109
mega M 106
kilo k 103
hecta h 102
deca da 101
SI BASE UNITS
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
To convert, using the following system: TO THE RIGHT multiply by 10
TO THE LEFT divide by 10
G M k h da SI BASE UNITS d c m μ n
DIVIDE BY 10
MULTIPLY BY 10
EXAMPLES:
1.6 m = ____________ μm
340 N = ____________ hN
EXAMPLES:
1250 cm = ____________ km
4.7 Gg = ____________ ng
In addition to using metric prefixes, we also convert between SI UNITS and other accepted systems of measurement.
Here are some helpful CONVERSION FACTORSyou should know when studying MOTION:
1 km = 1000 m
1 h = 3600 s1 m/s = 3.6 km/h
CONVERT THE FOLLOWING:
23 min = ____________ h
0.47 h= ____________ s
CONVERT THE FOLLOWING:
4.5 km/h = ____________ m/s
30.2 m/s = ____________ km/h
DO THE 2 ATTACHED WORKSHEETS in your handout for homework.
POINTS to REMEMBER:
Whatever you do to ONE SIDE of an EQUATION, you must do to the OTHER SIDE.
Do not move the item you are trying to isolate. Move EVERYTHING ELSE!!!
“Do the opposite” to move a variable. For example, to move a variable that is multiplied, divide by it.
Rearrange the following equations to solve for the variable indicated:
a = v Solve for v.t
y = mx + b Solve for m.
DO THE ATTACHED WORKSHEET in your handout for homework.
Accuracy measures how close a measurement is to an ACCEPTED or TRUE VALUE.
It is expressed as a PERCENT VALUE (%). Often, poor accuracy is a result of flaws in
equipment or procedure. EXAMPLE: Accepted Value ag = 9.80 m/s2
Experimental Value ag = 9.50 m/s2
Accuracy = 96.9 %
Precision measures the reliability, repeatability, or consistency of a measurement.
It is expressed as the accepted value ± a discrepancy.
Often, poor accuracy is a result of flaws in techniques by the experimenter.
EXAMPLE: Accepted Value ag = 9.80 m/s2
Experimental Value ag = 9.50 m/s2
Precision = 9.80 m/s2 ± 3.06
PRECISION: _________ACCURACY: _________
PRECISION: _________ACCURACY: _________
PRECISION: _________ACCURACY: _________
PRECISION: _________ACCURACY: _________
EXAMPLE:Describe the ACCURACY and PRECISION of each of the following results.
QUALITITATIVE DESCRIPTIONS Describing with words. These descriptions are made using the 5 senses. Example:
▪ colour of a solution▪ odor of a chemical product▪ sound of thunder
QUANTITATIVE DESCRIPTIONS Describing with numbers (i.e., quantities). These descriptions are made by counting and
measuring. Example:
▪ height of a building▪ speed of an airplane
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