This module contains the learning objectives for the chapter "Measurement and Geometry" from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, jr.
After completing this chapter, you should
know what the word measurement means
be familiar with United States system of measurement
be able to convert from one unit of measure in the United States system to another unit of measure
be more familiar with some of the advantages of the base ten number system
know the prefixes of the metric measures
be familiar with the metric system of measurement
be able to convert from one unit of measure in the metric system to another unit of measure
be able to convert an unsimplified unit of measure to a simplified unit of measure
be able to add and subtract denominate numbers
be able to multiply and divide a denominate number by a whole number
know what a polygon is
know what perimeter is and how to find it
know what the circumference, diameter, and radius of a circle is and how to find each one
know the meaning of the symbol π and its approximating value
know what a formula is and four versions of the circumference formula of a circle
know the meaning and notation for area
know the area formulas for some common geometric figures
be able to find the areas of some common geometric figures
know the meaning and notation for volume
know the volume formulas for some common geometric objects
be able to find the volume of some common geometric objects
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses the United States System of measurement. By the end of the module students should know what the word measurement means, be familiar with United States system of measurement and be able to convert from one unit of measure in the United States system to another unit of measure.
Measurement
The United States System of Measurement
Conversions in the United States System
There are two major systems of measurement in use today. They are the United States system and the metric system. Before we describe these systems, let's gain a clear understanding of the concept of measurement.
Measurement is comparison to some standard.
The concept of measurement is based on the idea of direct comparison. This means that measurement is the result of the comparison of two quantities. The quantity that is used for comparison is called the standard unit of measure.
Over the years, standards have changed. Quite some time in the past, the standard unit of measure was determined by a king. For example,
1 inch was the distance between the tip of the thumb and the knuckle of the king.
1 inch was also the length of 16 barley grains placed end to end.
Today, standard units of measure rarely change. Standard units of measure are the responsibility of the Bureau of Standards in Washington D.C.
Some desirable properties of a standard are the following:
Accessibility. We should have access to the standard so we can make comparisons.
Invariance. We should be confident that the standard is not subject to change.
Reproducibility. We should be able to reproduce the standard so that measurements are convenient and accessible to many people.
Some of the common units (along with their abbreviations) for the United States system of measurement are listed in the following table.
| Unit Conversion Table | |
| Length | 1 foot (ft) = 12 inches (in.) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5,280 feet |
| Weight | 1 pound (lb) =16 ounces (oz) 1 ton (T) = 2,000 pounds |
| Liquid Volume | 1 tablespoon (tbsp) = 3 teaspoons (tsp) 1 fluid ounce (fl oz) = 2 tablespoons 1 cup (c) = 8 fluid ounces 1 pint (pt) = 2 cups 1 quart (qt) = 2 pints 1 gallon (gal) = 4 quarts |
| Time | 1 minute (min) = 60 seconds (sec) 1 hour ( hr) = 60 minutes 1 day (da) = 24 hours 1 week (wk) = 7 days |
It is often convenient or necessary to convert from one unit of measure to another. For example, it may be convenient to convert a measurement of length that is given in feet to one that is given in inches. Such conversions can be made using unit fractions.
A unit fraction is a fraction with a value of 1.
Unit fractions are formed by using two equal measurements. One measurement is placed in the numerator of the fraction, and the other in the denominator. Placement depends on the desired conversion.
Place the unit being converted to in the numerator.
Place the unit being converted from in the denominator.
For example,
| Equal Measurements | Unit Fraction |
| 1ft = 12in. |
|
| 1pt = 16 fl oz |
|
| 1wk = 7da |
|
Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.
Convert 11 yards to feet.
Looking in the unit conversion table under length, we see that
1 yd =3 ft. There are two corresponding unit fractions,
and
. Which one should we use? Look to see which unit we wish to convert to. Choose the unit fraction with this unit in the numerator. We will choose
since this unit fraction has feet in the numerator. Now, multiply 11 yd by the unit fraction. Notice that since the unit fraction has the value of 1, multiplying by it does not change the value of 11 yd.
Thus, 11 yd =33ft.
Convert 36 fl oz to pints.
Looking in the unit conversion table under liquid volume, we see that 1 pt = 16 fl oz. Since we are to convert to pints, we will construct a unit fraction with pints in the numerator.
Thus, 36 fl oz = 2.25 pt.
Convert 2,016 hr to weeks.
Looking in the unit conversion table under time, we see that 1wk =7da and that 1 da = 24 hr. To convert from hours to weeks, we must first convert from hours to days and then from days to weeks. We need two unit fractions.
The unit fraction needed for converting from hours to days is
. The unit fraction needed for converting from days to weeks is
.
Thus, 2,016 hr = 12 wk.
Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.
Convert 18 ft to yards.
Convert 2 mi to feet.
Convert 26 ft to yards.
Convert 9 qt to pints.
Convert 52 min to hours.
Convert 412 hr to weeks.
Make each conversion using unit fractions. If fractions occur, convert them to decimals rounded to two decimal places.
14 yd to feet
3 mi to yards
8 mi to inches
2 mi to inches
18 in. to feet
84 in. to yards
5 in. to yards
106 ft to miles
62 in. to miles
0.4 in. to yards