8.1+US+Measurement

Section 8.1 - US Measurement
We measure things with units. Money is measured in dollars and cents. Distances with inches, feet, miles, and a few others. Weight is often pounds, but could also be ounces or tons. The units of measurement vary depending on what they measure, but they are usually mathematically related within the type of unit. For example, there are 12 inches in every foot and 3 feet in every yard.

Some units are more applicable to a particular situation than others. For example, we would likely measure a person's weight in pounds, but it could conceivably be done in ounces or tons. In order to convert from one unit to another, you need to know how the units mathematically compare.


 * Conversion Factor or Rate **- The mathematical relationship between different units, often expressed as a ratio (fraction).


 * Basic US Conversion Rates**

__Length or Distance__

12 inches = 1 foot 3 feet = 1 yard 5280 feet = 1 mile

__Weight or Mass__

16 ounces = 1 pound 2000 pounds = 1 ton

__Volume (liquid)__

8 ounces = 1 cup 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon

Notice that the range between any two levels is not consistent. There is a big difference between pounds and tons, but not so much between ounces and pounds. Notice also, that the multiplier from one unit to the next is also not consistent -- 12 inches to a foot, but only 3 feet to a yard, then 16 ounces to a pound.


 * Converting between Units**

There are two ways to convert between units, such as converting 9.3 feet to inches. Both methods use the conversion unit.

__Method 1: Multiply or Divide by the Conversion Rate__

This is a critical concept to understand: If the unit is larger, you will need fewer of them. In one yard, there are 36 inches, but only 3 feet. As you work through method 1, you will see that if you increase the number, you decrease the unit size. If you are converting from a smaller unit (inches) to a larger one (feet), you will actually divide and the number (of feet in this case) will be smaller than you started with (fewer feet to equal the same length in inches).

42 inches --> ? feet

To convert 42 inches to feet, you will divide 42 by the conversion rate - by 12 because there are 12 inches in a foot. 42 divided by 12 is 3.5, so 42 inches = 3.5 feet.

5.2 pounds --> ? ounces

To convert 5.2 pounds to ounces, multiply 5.2 by the conversion rate that compares ounces and pounds (16 ounces = 1 pound). 5.2 times 16 is 83.2, so 5.2 pounds = 83.2 ounces.

2 gallons = ? cups

Sometimes you need to convert multiple times to get to the target unit of measurement. 2 gallons times 4 (quarts in a gallon) times 2 (pints in a quart) times 2 (cups in a pint) = 32 cups.

__Method 2: Multiply by the Conversion Factor (Ratio)__



A conversion factor as a ratio (fraction) is always equal to 1 because the value of the numerator is the same as the value of the denominator, even though they don't look the same. Notice that it doesn't really matter in this case which unit is the numerator. However, it really does matter which you use to do the math, because only one will give the correct answer. The trick is simply to pick the right one.


 * To convert from one unit to another, multiply by the conversion factor that has the starting units as the denominator and the ending units as the numerator. **



This video converts between US and metric units, but the process is exactly the same.

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 * Chapter Eight Practice Problems**

**Where to from here?**
8.1 US Measurement 8.2 Metric Measurement 8.3 US to Metric Chapter Eight Summary Chapter Eight Homework