Metric Prefixes & Unit ConversionsUsing the Factor Label Method

Scientific Notation• 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

• = 0.983

Scientific Notation: Practice

• 34,000,000 =

• 7.29 x 10 5

=

• 0.3254 =

• 5.6 x 10 -3 =

3.4 x 10 7

729,000

3.254 x 10 -1

0.005600

Metric Prefixes

IMPORTANT: MEMORIZE THESE

Metric Prefixes

1 meter = 100 centimeters1 gram = 1000 miligrams

1 gram = 0.001 kilograms1 kilogram = 1000 grams

Unit Conversions

• Changing one unit of measurement to another•Converting hours to minutes, for exampleOR…• Miles to kilometers • Meters to feet• Liters to milliliters• Etc…

Factor Label Method: How many meters are there in a kilometer?

• 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

𝟏𝒌𝒎𝟏

Whoa! HOLD ON…..!!

Conversion Factor• Multiplication – ok to multiply by “1”

𝟏𝒉𝒓𝟏 𝟏𝒉𝒓

𝟏

𝟏𝒉𝒓𝟏 𝟏𝒉𝒓

𝟏

𝟏𝒉𝒓𝟏

𝟔𝟎𝒎𝒊𝒏𝟏

Factor Label Method: How many meters are there in a kilometer?• 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

𝟏𝒌𝒎𝟏

𝟏𝟎𝟎𝟎𝒎𝟏𝒌𝒎

𝟏𝟎𝟎𝟎𝒎𝟏

1000m

× = =

Factor Label Method: How many miles are there in 5 kilometers?

• 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

𝟓𝒌𝒎𝟏

𝟏𝒎𝒊𝟏 .𝟔𝟏𝒌𝒎

X𝟓𝒎𝒊𝟏 .𝟔𝟏= 3.11

mi=

Again: 1.3 kg = ___ g?

3 kg1000

g   

3000 g1 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.

And again: 15.2 cm = ___ m?

15.2 cm 1 m  

0.152 m1

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. • 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.

Again – with a twist: 4300 m = ___ miles?

• 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.

𝟒𝟑𝟎𝟎𝒎𝟏

𝟏𝒌𝒎𝟏𝟎𝟎𝟎𝒎

𝟏𝒎𝒊𝟏 .𝟔𝟏𝒌𝒎 2.8

milesx x =

Factor Label Method:60 mi/hr is how many km/sec?• 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: Simplify𝟔𝟎𝒎𝒊𝟏𝒉𝒓

𝟏 .𝟔𝟏𝒌𝒎𝟏𝒎𝒊

𝟏𝒉𝒓𝟔𝟎𝒎𝒊𝒏

𝟏𝒎𝒊𝒏𝟔𝟎 𝒔𝒆𝒄

𝟗𝟔 .𝟔𝒌𝒎𝟑𝟔𝟎𝟎𝒔𝒆𝒄

𝟎 .𝟎𝟐𝟕𝒌𝒎𝒔𝒆𝒄X XX ==