Using the Factor Label Method
• Easier way to write very large and very small numbers
• 983,000,000 = 9.83 x 10 8
• 0.00000983 = 9.83 x 10 -6
• Takes advantage of the fact that:
• Multiplying by 10, moves the decimal point one place to the right
• 9.83 x 10 = 98.3
• Dividing by 10, moves the decimal point one place to the right
•
9.83
= 0.983
10
• 34,000,000 = 3.4 x 10 7
• 7.29 x 10 5 = 729,000
• 0.3254 = 3.254 x 10 -1
• 5.6 x 10 -3 = 0.005600
IMPORTANT: MEMORIZE THESE
1 meter = 100 centimeters
1 gram = 1000 miligrams
1 gram = 0.001 kilograms
1 kilogram = 1000 grams
• Changing one unit of measurement to another
• Converting hours to minutes, for example
OR…
• Miles to kilometers
• Meters to feet
• Liters to milliliters
• Etc…
• Step 1: Start with what you start with
• Turn it into a fraction by placing your known measurement over “1”
• Step 2: multiply by a conversion factor
Whoa! HOLD ON…..!!
𝟏𝒌𝒎
𝟏
• Multiplication – ok to multiply by “1”
𝟏𝒉𝒓
𝟏𝒉𝒓
𝒙𝟏=
𝟏
𝟏
𝟏𝒉𝒓
𝒙
𝟏
𝟒
𝟒
𝟏𝒉𝒓
𝟏
𝟔𝟎 𝒎𝒊𝒏
𝟏 𝒉𝒓
𝒙
𝟏𝒉𝒓
=
𝟏
𝟔𝟎 𝒎𝒊𝒏
=
𝟏
• Step 1: Start with what you start with
• Turn it into a fraction by placing your known measurement over “1”
• Step 2: multiply by a conversion factor
• Numerator to denominator – keep the same units so they cancel
• Step 3: Multiply the fraction
• Step 4: Simplify
𝟏𝒌𝒎
𝟏
𝟏𝟎𝟎𝟎𝒎
×
𝟏𝒌𝒎
𝟏𝟎𝟎𝟎𝒎
=
𝟏
=
1000m
• Step 1: Start with what you start with
• Turn it into a fraction by placing your known measurement over “1”
• Step 2: multiply by a conversion factor
• Numerator to denominator – keep the same units so they cancel
• Step 3: Multiply the fraction
• Step 4: Simplify
𝟓𝒌𝒎
𝟏
X
𝟏 𝒎𝒊
𝟏. 𝟔𝟏 𝒌𝒎
=
𝟓 𝒎𝒊
𝟏. 𝟔𝟏
=
3.11 mi
• Start with what you start with and set it over “1”.
• Find your conversion factor and insert it so that the original
units cancel.
• Notice that the kg in my conversion factor is in the
denominator to cancel!
• Cancel the units, and then multiply the top of the tracks
and then divide by the bottom of the tracks.
3 kg
1000 g
3000 g
1
1 kg
• Start with what you start with and set it over “1”.
• Find your conversion factor and insert it so that the original
units cancel.
• Notice that the kg in my conversion factor is in the
denominator to cancel!
• Cancel the units, and then multiply the top of the tracks
and then divide by the bottom of the tracks.
15.2 cm
1m
0.152 m
1
100 cm
• Start with what you start with and set it over “1”.
• Find your conversion factor and insert it so that the original
units cancel.
• If you don’t have one conversion factor that gets you to
the units you need, see what steps you can take to get
there.
𝟒𝟑𝟎𝟎 𝒎 𝟏 𝒌𝒎
x
𝟏
𝟏𝟎𝟎𝟎 𝒎
x
𝟏 𝒎𝒊
𝟏. 𝟔𝟏 𝒌𝒎
=
2.8 miles
• Double decker problem
• Same procedure – just take on deck at a time…
• Step 1: Start with what you start with
• It’s already a fraction! (“per” means divide!)
• Step 2: multiply by a conversion factor
• Pick the numerator or denominator – either one; they both get done anyway…
• Numerator to denominator – keep the same units so they cancel
• Step 3: Multiply the fractions
• Step 4: Simplify
𝟔𝟎 𝒎𝒊
𝟏. 𝟔𝟏 𝒌𝒎
X
X
𝟏 𝒉𝒓
𝟏 𝒎𝒊
𝟏 𝒉𝒓
𝟔𝟎 𝒎𝒊𝒏
X
𝟗𝟔. 𝟔 𝒌𝒎
𝟎. 𝟎𝟐𝟕 𝒌𝒎
𝟏 𝒎𝒊𝒏
=
=
𝟑𝟔𝟎𝟎 𝒔𝒆𝒄
𝒔𝒆𝒄
𝟔𝟎 𝒔𝒆𝒄