Drill 923

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Drill 9/23

• How many seconds are in 9.7 hours?
• 2. How did you figure out that answer?

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SI Units, Metric Conversions, Dimensional
Analysis
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• A major theme of science is communication and
  collaboration. We need a single measurement
  system for everyone.
• Le Systeme International dUnites - SI

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SI UNITS
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• We use SI prefixes to represent quantities that
  are larger or smaller than the base units.

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Dimensional Analysis

• Dimensional Analysis is a method used to make
  conversions. This method helps us organize
  information without becoming confused about what
  units are being cancelled or multiplied/divided.

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Rules

• You must use Dimensional Analysis to solve
  conversion problems
• Always show all your work
• Include units
• Make sure your units cancel out
• Everything on the top is multiplied
• Everything on bottom is divided from the top

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Conversion Factors

• A ratio (or fraction) derived from the equality
  between two different units that can be used to
  convert from one unit to the other.
• Conversion factors always equal one because the
  two values are equal to each other.

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Conversion Factors
4 quarters
1 dollar
1
1
1 dollar
4 quarters
60 minutes
1 hour
1
1
1 hour
60 minutes
1 m
100 cm
1
1
100 cm
1 m
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Convert 62.0 inches to centimeters

• First we need to map out what we are doing.
• 62.0 in ? ___ cm

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Convert 62.0 inches to centimeters

• Second we need to determine our conversion factor
• How many centimeters are in one inch?
• 2.54 cm 1 in

1 in
2.54 cm
Note We could have also used that 1cm .394
inch but as a general rule, the larger unit gets
the 1!
1
1
2.54 cm
1 in
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Convert 62.0 inches to centimeters

• Third, we multiply our given by the conversion
  factormaking sure to arrange the conversion
  factor so that the units CANCEL!

62.0 in
2.54 cm
X
157.48 cm
1 in
Note Units that are both on the top and the
bottom cancel
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Convert 62.0 inches to centimeters

• Lastly, we make sure that we reached our
  destination and that we have the correct number
  of significant figures.

157.48 cm ? 157 cm
Note Conversions factors do not follow
significant figure rules, they are not measured
and do not show accuracy.
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Multiple Conversions

• When conversions require several steps,
  Dimensional Analysis is extremely useful. It
  helps organize information so we can think
  through problems step-by-step.

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How many feet are in 965 cm?

• 1. Map it out 965 cm ? ___ ft
• 2. Find conversion factors

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How many feet are in 965 cm?
965 cm
1 in
1 ft
X
31.66 ? 31.7 ft
X
2.54 cm
12 in
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• You are cooking for a large group of people.
  You must change the recipe to accommodate all the
  guests. How many gallons will 384 teaspoons of
  vanilla extract occupy?
• 1 Tablespoon (T) 3 teaspoons (t)
• 1 cup (c) 16 Tablespoons
• 1 pint (pt) 2 cups
• 1 quart (qt) 2 pints
• 1 gallon (gal) 4 quarts