Metric Conversions, Dimensional Analysis, and Scientific Notation
DIMENSIONAL ANALYSIS FACTOR-LABEL CONVERSIONS
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DIMENSIONAL ANALYSISFACTOR-LABELCONVERSIONS
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Basic Measurement• A quantitative measurement always consists of a
number and a unit. • A qualitative observation simply makes a statement.
• Two major systems are used today:English System – used in US onlyMetric System (SI SYSTEM) - used by rest of the world
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FUNDAMENTAL SI UNITS
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Stair Step method
Kilo- (K) 1000 Hecto- (H) 100 Deka- (D) 10 base units Deci- (d) .1 Centi- (c) .01 Milli- (m)
.001
Grams, liters, meters
If you know left from right ANDIf you can count …. YOU CAN CONVERT!
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PRACTICE• 525568 mm = ? m
• 0.00654 km = ? m
525.568 m
Start on mm … Move three …To the Left
6.54 m
Start on km… Move three … To the Right
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Equivalent Values• Open the bag and find equivalent values related
to familiar items. • Can you arrange them? • Are the measurements equivalent?
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• 1 can equivalent to 3 balls 1 can = 3 balls
• 1 can per 3 balls 1 can 3 balls
English to Math Translations
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• 1 loaf equivalent to 24 slices 1 loaf = 24 slices
• 1 loaf per 24 slices1 loaf24 slices
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• 1 carton equivalent to 12 eggs 1 carton = 12 eggs
• 1 carton per 12 eggs12 eggs 1 carton
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CONVERSIONS• Use equivalent values to move from one measurement
to another 1 dozen eggs = 12 eggs ….. 12 eggs = 1 dozen
• Using fractions, this can be expressed:1 dozen OR 12 eggs
12 eggs 1 dozen
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CALCULATE• Calculate how many seconds are in a school
day (from 8:00 to 3:00).
• Calculate your height in centimeters. (1 inch = 2.54 cm, 12 inches = 1 foot)
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FACTOR-LABEL HINTS
• START with what is given (amount and unit)• END with what you are trying to get to (unit)• MAKE SURE YOUR UNITS CANCEL ALONG THE WAY!• * Smaller number goes with larger unit. • * Larger number goes with smaller unit.
1 elephant = 40,000 mice
USE RAILROAD TRACKS!
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FACTOR-LABEL EXAMPLE• You're throwing a pizza party for 15 people. • Each person will eat 4 slices. • Each pizza costs $14.50 and has 12 slices per pizza. • How much is the pizza going to cost you?
• Arrange pizza equivalences from bag.
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RAILROAD: Factor-Label MethodSTART: by writing down given
given
1 party
party
NEXT: bring down given unitNEXT: THINK and LINK
people
1
15
NEXT: cancel and continue