A way to solve math problems in science Used to convert km to miles, m to km, mol to g, g to mol, etc. To use this we need: 1) desired quantity, 2) given

• A way to solve math problems in science• Used to convert

km to miles, m to km, mol to g, g to mol, etc.• To use this we need: 1) desired quantity, 2)

given quantity, 3) conversion factors• Conversion factors are valid relationships or

equities expressed as a fractionE.g. for 1 km=0.6 miles the conversion factor is

The factor label method

km 1

miles 0.6 or

miles 0.6

km 1

Q. write conversion factors for 1 foot =12 inchesQ. what conversion factors can you think of that

involve meters?

Conversion factorsConversion factors for 1 ft = 12 in

foot 1

inches 12 or

inches 12

foot 1

There are almost an infinite number of conversion factors that include meters:

mm 1000

m 1 ,

cm 100

m 1 ,

km 1

m 1000

m 1

yards 0.9144 ,

inches 39.37

m 1 ,

feet 3.28

m 1

The steps to followNow we are ready to solve problems using the

factor label method. The steps involved are:

1. Write down the desired quantity/units

2. Equate the desired quantity to given quantity

3. Determine what conversion factors you can use (both universal and question specific)

4. Multiply given quantity by the appropriate conversion factors to eliminate units you don’t want and leave units you do want

5. Complete the math

Factor label exampleQ - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

First write down the desired quantity

# km

Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles)

Next, equate desired quantity to the given

quantity

# km = 47 mi

Factor label example


Now we have to choose a conversion

factor

# km = 47 mi



What conversion factors are possible?

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Pick the one that will allow you to cancel

out miles

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km


Pick the one that will allow you to cancel

out miles


# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47 mi x 1 km 0.621 mi



Cross out common factors

# km = 47 mi x 1 km 0.621 mi



Cross out common factors

# km = 47 x 1 km 0.621



Are the units now correct?

# km = 47 x 1 km 0.621



Yes. Both sides have km as units.

# km = 47 x 1 km 0.621



Yes. Both sides have km as units.

= 47 x 1 km 0.621

# km



Now finish the math.

# km = 47 x 1 km 0.621

= 75.7 km



The final answer is 75.7 km

# km = 47 x 1 km 0.621

= 75.7 km


Summary

The previous problem was not that hard

In other words, you probably could have done it faster using a different method

However, for harder problems the factor label method is easiest

More examples1. You want to buy 100 U.S. dollars. If the

exchange rate is 1 Can$ = 0.65 US$, how much will it cost?

# Can$ = 100 US$ x 1 Can$ 0.65 US$

= 153.85 Can$

More examples2. There are 12 inches in a foot, 0.394 inches in a centimeter, and 3 feet in a yard. How many cm are in one yard?

# cm = 1 yd x 3 ft 1 yd

= 91.37 cmx 12 in

1 ft x 1 cm

0.394 in

AssignmentAnswer questions using the factor label method:1. Calculate how many feet are in 1 meter (use

information from the examples above.2. How many decimeters are in 2 kilometers?3. Show how many mL are in 1 L?4. If Nogales is 35.34 miles from Sahuarita,

calculate how far that is in km. (1km=0.62mi)

5. Now calculate how many cm Nogales is from Sahuarita.

Documents

A way to solve math problems in science Used to convert km to miles, m to km, mol to g, g to mol, etc. To use this we need: 1) desired quantity, 2) given