Unit Conversions

In this lesson, we will examine how to convert from one system of units to another.  For the CAHSEE, you do not need to memorize most of the conversion factors, but you do need to be able to apply the appropriate conversion factor when necessary.  There are some conversion factors you will need to remember.  Below is a table of some of the conversion factors that you should attempt to memorize.  It includes some of the units from the system generally used in the United States and the metric system that is used in the rest of the world and in science.

U.S. Customary

Metric

1 foot =  12 inches 1 kilometer  =  1000 meters
1 yard  =  3 feet 1 meter  =  1000 millimeters
1 hour  =  60 minutes 1 meter  =  100 centimeters
1 minute  =  60 seconds 1 kilogram  =  1000 grams
1 pound  =  16 ounces 1 gram  =  1000 milligrams
  1 kiloliter  =  1000 liters
  1 liter  =  1000 milliliters

Notice that the metric system uses meters for length, grams for weight, and liters for fluid volume.  If you remember the three prefixes:  kilo-, centi-, and milli-, then you can handle most of the questions that the CAHSEE will ask you that involve the metric system conversion. 


Example 1

10 meters is...

A.  100  millimeters       B.  1000 millimeters        C.  1/100 kilometers        D.  1/1000 kilometers

Solution

First notice that since there are 1000 millimeters in a meter, to find out how many millimeters there are in 10 meters, we multiply:

        (10 meters)(1000 millimeters per meter)  =  10,000 millimeters

None of the possible answers matches this, so we need to convert to kilometers.  Since

        1 kilometer = 1000 meters

we can divide by 1000 to conclude that

        1 meter  =  1/1000 kilometers

We want 10 meters, so we multiply by 10 to get

        (10 meters)(1/1000 kilometers per meter)  =  10/1000 kilometers

This fraction reduces to 1/100, so the solution is C.


Now try one by yourself.  If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear.

Exercise 1

1/10 liter is

A.  1000 milliliters    B.  100 milliliters    C.  1/100 of a kiloliter    D.  1/1000 of a kiloliters

Answer:

        B.  100 milliliters


Example 2

It took Paul 5 hours to drive from Los Angeles to Las Vegas.  How many seconds did it take him?

Solution

We are asked to convert from hours to seconds.  The strategy that we will take is to first find out how many minutes it took him and then convert from minutes to seconds.  Since there are 60 minutes in an hour, we can find how many minutes it took him by multiplying by 60.

        (5 hours)(60 minutes per hour)  =  300 minutes

We just need to convert to seconds.  Since there are 60 seconds in a minute we can convert to seconds by multiplying by 60.

        (300 minutes)(60 seconds per minute)  =  18,000 seconds

It took Paul 18,000 seconds to drive from Los Angeles to Las Vegas.


Now try one by yourself.  If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear.

Exercise 2

Lilliana took a measurement of the length of her apartment and found it to be 33 feet 9 inches.  How many yards is the apartment's length?  (Hint:  you will want to convert 33 feet to yards and 9 inches to yards.  Then add the results.)

Answer:

      11.25 or 11 1/4 yards


Conversions Between Systems

We have seen how to convert within the U.S. system and within the metric system.  Now we will explore converting from one system to another.  Below is a table of some of the most common unit conversions.  You do not need to memorize these for the CAHSEE.  The exam always provides the student with these conversion factors when needed.

  Metric to U.S. Customary U.S. Customary to Metric
Length 1  cm  ≈  0.4 in.

1 m  ≈  1.1 yd

1 km  ≈  0.62 mi

1 in.  ≈  2.54 cm

1 yd  ≈  0.91 m

1 mi  ≈  1.6 km

Weight 1 g  ≈  0.35 oz

1 kg  ≈  2.2 lb

1 oz  ≈  28 g

1 lb  ≈  0.45 kg

Capacity 1 mL  ≈  0.034 fl oz

1 L  ≈  1.06 qt

1 fl oz  ≈  30 mL

1 qt  ≈  0.95 L

When you are asked to convert, you will need to either multiply or divide by the conversion factor.  We will next go over some examples.


Example 3

Jose is driving at 60 miles per hour.  What is his approximate speed in kilometers per hour?  (1 mile   ≈  1.6 km).

Solution

To convert from miles per hour to kilometers per hour, we need to change the miles to kilometers.  The "per hour" part does not need to be converted since our answer is also required to include "per hour".  We have

        (60 miles)(1.6 km per mile)  =  96 km

Hence, 60 miles per hour is the same as 96 kilometers per hour.  Jos is driving 96 kilometers per hour.


Example 4

Roger is 2 meters tall.  How tall is he in feet and inches?  (1 meter  ≈  39 inches)

Solution

First convert meters to inches.  We have

        (2 meters)(39 inches per meter)  =  78 inches

We are not finished yet, since we need to convert to feet and inches.  To find our how many feet and inches, we know that there are 12 inches in 1 foot.  We can divide 78 inches by 1 foot per 12 inches to get

        78/12  =  6 with a remainder of 6.

Notice that

        6 feet = 72 inches

which leaves 6 additional inches.  In other words Roger is 6 feet 6 inches tall.


Now try one by yourself.  If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear.

Exercise 3

One cubic centimeter is approximately equal to 0.061 cubic inches.  Approximately how many cubic inches are there in 24 cubic centimeters?

Answer:

        1.464 cubic inches