Transcript Dimensional Analysis

DIMENSIONAL ANALYSIS
Dimensional Analysis
 What happens when you divide a number by
itself?
 What happens when you divide a unit by
itself?
 In both cases, you get the number 1.
 Dimensional analysis involves multiplication
and division.
 Focus on cancelation of UNITS
 Just another method of unit conversion
Conversion factors
 To convert between units:
 Figure out what CONVERSION FACTOR you
need to perform your calculation
 Conversion factors – take a definition and turn it
into a fraction equal to one – for example:
 There are 12 inches in 1 foot
 12 inches
or 1 foot
1 foot
12 inches
Examples of dimensional
analysis
Multiply across the top. Divide by whatever’s on the bottom
Examples of dimensional
analysis
 Convert 2.6 km to mm
 First- what is the desired unit?
 Answer- mm
 Second- how to we get from m to mm?
 We know that 1 km = 1000 m
 We know that 1 m = 1000 mm
 2.6 km( 1000 m )(1000 mm) = 2600000 m
1 km
1m
Scientific Notation
 Why do we need to know this?
 It’s hard to work with numbers like this:
 6,000,000,000,000,000,000,000
 Or this 0.00000000000000000000876
 What is scientific notation?
 Simplifying large or small numbers by converting
them to a number between 1 and 10 multiplied by
powers of 10
Scientific Notation
 Powers of 10?
 10 x 10 x 10 = 1000 or 103
 10-n = 1/10n
 So
10-3 = 1/103 = 1/1000 = 0.001
Converting regular notation
to Scientific Notation
 Always move the decimal so there is one
number LEFT of the decimal
 If the original number is LARGER than 1 and the
decimal is moved to the LEFT, use a positive
exponent
 1,567 = 1.567 x 103
 If the original number is SMALLER than 1 and the
decimal is moved to the RIGHT, use a negative
exponent
 0.0000045 = 4.5 x 10-6
Converting from scientific
notation to regular notation
 Move the decimal the number of places
indicated by the exponent.
 If the exponent is positive, your final number
should be larger than 1
 5.6 x 102 = 560
 I f the exponent is negative, your final number
should be smaller than 1
 5.6 x 10-2 = 0.056