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