Using the Factor Label Method

“That costs five.”

As long as we have different units… And we always will…. WE NEED TO KNOW HOW TO CONVERT BETWEEN THEM!

we need it to have values that are universally accepted and meaningful.

Allows scientists to compare values directly (“apples to apples”) You don’t have to memorize or look up conversion factors You can check if your problem solving approach is correct Scientists can check that an equation is “physically meaningful” by being sure that the units on both sides of the equation are the same.

MARS CLIMATE ORBITER LOST! “…findings indicate that one team used English units (e.g., inches, feet and pounds) while the other used metric units for a key spacecraft operation. This information was critical to the maneuvers required to place the spacecraft in the proper Mars orbit.”

The engine fired but the spacecraft came within 60 km (36 miles) of the planet -- about 100 km closer than planned and about 25 km (15 miles) beneath the level at which the it could function properly, mission members said. That probably stopped the engine from completing its burn, so Climate Orbiter likely plowed through the atmosphere, continued out beyond Mars and now could be orbiting the sun…

IMPORTANT: MEMORIZE THESE 1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm

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: Turn your starting value into a fraction by putting it over “1” Step 2: multiply by a conversion factor Whoa! HOLD ON…..!!

Multiplication – ok to multiply by “1”

The measurements must be equal to each other. Let’s try it!

1.Turn known measurement into a fraction (set over “1”) 2.Pick a conversion factor: FROM units TO different units 3.Decide which “form” of the conversion factor to use – Which one goes on the top? 4.Cross out the units that have one in the numerator (top) and one in the denominator (bottom) 5.Multiply all the numbers in the numerators (top). Multiply all the numbers in the denominators (bottom). 6.Simplify – Do the math!

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 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 X = 3.11 mi =

3 kg 1000 g 3000 g 11 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 cm1 m m 1100 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.

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. 2.8 miles xx=

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 X X X = =

34,000,000 = 7.29 x 10 5 = = 5.6 x = 3.4 x , x

1 meter = 100 centimeters 1 gram = 1000 miligrams 1 gram = kilograms 1 kilogram = 1000 grams