Transcript GETTING FROM ONE UNIT TO ANOTHER: Dimensional Analysis

GETTING FROM ONE UNIT TO
ANOTHER:
Dimensional Analysis
aka. Factor Labeling Method
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The answer is 12.
• 12 of ???????
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You must indicate the units for
a number to be meaningful.
• 150 pounds is not equal to 150 kg.
• With no unit, a numerical answer is incorrect!
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Conversion factors
• A conversion factor is used to move from one unit to the
other.
• We use a conversion factor by showing equivalent
amounts in each unit, one over the other.
– The top must be equal to the bottom.
– Write the unit on bottom that you need to cancel out, or get rid of.
• Example: 12 eggs = 1 dozen eggs
12 eggs
1 dozen eggs
How many eggs in 4 dozen?
4 dozen 12 eggs
= 48 eggs
1 dozen
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Steps in Dimensional
Analysis
•
•
•
•
Identify needed conversion factor.
Write what you have.
Draw a grid to separate each factor.
Write first conversion factor so that the unit you
want to cancel out is on bottom.
• Cross out units (NOT the numbers) as they
cancel out.
• When the top unit is what you want, multiply the
numbers on top of grid, then divide by each
number on the bottom of grid.
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Dimensional Analysis Example: What is the
weight of a 201 pound person in kg?
• Identify needed conversion factor.
2.2 lb = 1 kg
201 lb
• Write what you have.
• Draw a grid to separate each factor.
• Write first conversion factor so that the unit you want to cancel
out is on bottom.
201 lb
1 kg
2.2 lb
• Cross out units (NOT the numbers) as they cancel out.
• When the top unit is what you want, multiply the numbers on
top of grid, then divide by each number on the bottom of grid.
201 lb 1 kg = 201 kg
2.2 lb
2.2
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= 91.4 kg
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Dimensional Analysis Example: How many
km/sec is the same as 55 miles per hour?
1 km = 0.62 mile
60 min = 1 hour
60 sec = 1 min
55 mile 1 km
1 hr
1 min
hr
0.62 mile 60 min 60 sec
55 km x 1
x1 x1
0.62 x 60 x 60 sec
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=
= 0.025 km
sec
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Significant Figures
• All digits 1-9 inclusive are significant.
• Zeros between significant digits are always significant.
– Example: 5.007 has 4 significant figures.
• If a number contains a decimal point, all zeros and digits are
significant after & including the first digit 1-9.
– Trailing zeros in a number are significant in a number only if the
number contains a decimal point.
100.0 has 4 sig. figs.
Ex: 100 has 1 sig. fig.
– Zeros in the beginning of a number whose only function is to
place the decimal point are not significant.
Ex: 0.0025 has 2 sig. figs.
– Zeros following a decimal significant figure are significant.
Ex: 0.000470 has 3 sig. figs.
Ex: 0.47000 has 5 sig. figs.
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Scientific Notation 1
• Example 1: Convert 1 500 000 to scientific notation.
Move the decimal point so that there is only one digit to its
left (a total of 6 places).
1 500 000 = 1.5 x 106
• Example 2: Convert 0.00025 to scientific notation.
Move the decimal point 4 places to the right.
0.00025 = 2.5 x 10-4
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Scientific Notation 2
• Example 3: Correct 12 x 108 to proper scientific
notation.
Move the decimal one place to the left. Add to exponent
when decimal moves left; subtract from the exponent
when decimal moves right (ALSR).
12 x 108 = 1.2 x 109
• Example 4: Correct 0.0040 x 10-8 to proper scientific
notation.
Subtract from the exponent when decimal moves right, so 8 -3 = -11.
0.0040 x 10-8 = 4.00 x 10-11
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