1.10 Systems of Measurement

Learning Objectives

By the end of this section, you will be able to:

  • Make unit conversions in the US system
  • Use mixed units of measurement in the US system
  • Make unit conversions in the metric system
  • Use mixed units of measurement in the metric system
  • Convert between the US and the metric systems of measurement
  • Convert between Fahrenheit and Celsius temperatures

Make Unit Conversions in the U.S. System

There are two systems of measurement commonly used around the world. Most countries use the metric system. The U.S. uses a different system of measurement, usually called the U.S. system. We will look at the U.S. system first.

The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart, and gallons. Both the U.S. system and the metric system measure time in seconds, minutes, and hours.

The equivalencies of measurements are shown in Table 1.58. The table also shows, in parentheses, the common abbreviations for each measurement.

A table is given with three columns. In the first column are directions. The second column has exposition, and the third column has the mathematical steps. In the first row, the direction is “Step 1. Multiply the measurement to be converted by; write as a fraction relating the units given and the units needed.” The exposition is “Multiply inches by, writing as a fraction relating inches and feet. We need inches in the denominator so that the inches will divide out!” The mathematical step is 66 inches times the fraction (1 foot) over (12 inches).
In the following row, we have “Step 2. Multiply.” The hint is “Think of 66 inches as the quantity 66 inches divided by 1.” The math portion is the fraction (66 inches times 1 foot) over 12 inches.
In the following row, we have “Step 3. Simplify the fraction.” The hint is that “Notice: inches divide out.” We obtain 66 feet divided by 12.
Then the last step is “Step 4. Simplify.” The hint is “Divide 66 by 12.” Hence, our final mathematical statement is 5.5 feet.

When we use the identity property of multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.

Sometimes, to convert from one unit to another, we may need to use several other units in between, so we will need to multiply several fractions.

Convert Between the U.S. and the Metric Systems of Measurement

Many measurements in the United States are made in metric units. Our soda may come in 2-liter bottles, our calcium may come in 500-mg capsules, and we may run a 5K race. To work easily in both systems, we need to be able to convert between the two systems.

Table 1.62 shows some of the most common conversions.

Figure 1.22 shows how inches and centimeters are related on a ruler.

A ruler with inches and centimeters.

Figure 1.22 This ruler shows inches and centimeters.

Figure 1.23 shows the ounce and milliliter markings on a measuring cup.

A measuring cup showing milliliters and ounces.

Figure 1.23 This measuring cup shows ounces and milliliters.

Figure 1.24 shows how pounds and kilograms marked on a bathroom scale.

We are given an image of a bathroom scale showing pounds.

Figure 1.24 This scale shows pounds and kilograms.

We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.

Two thermometers are shown, one in Celsius (°C) and another in Fahrenheit (°F). They are marked “Water boils” at 100°C and 212°F. They are marked “Normal body temperature” at 37°C and 98.6°F. They are marked “Water freezes” at 0°C and 32°F.

Figure 1.25 The diagram shows normal body temperature, along with the freezing and boiling temperatures of water in degrees Fahrenheit and degrees Celsius.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.This is a table that has seven rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “define US units of measurement and convert from one unit to another,” “use US units of measurement,” “define metric units of measurement and convert from one unit to another,” “use metric units of measurement,” “convert between the US and the metric system of measurement,” and “convert between Fahrenheit and Celsius temperatures.” The rest of the cells are blank.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?