CHAPTER 4 Measurement and Measurement Tools CONTENTS 1 Units of Measure 2 Measurement Tools and How to Read Them 3 Measurements on Scale Drawings 168 INTRODUCTION Accurate measurement is critical to the success of many jobs performed by UBC members. Measuring lines, shapes, and angles is a fundamental skill OBJECTIVES in the building trades. This chapter discusses units of measure and how to Upon successful completion convert measurements from one unit of measure to another. The chapter of this chapter, the also describes some of the most commonly used measurement tools, how participant should be they are used, and their particular advantages. The chapter concludes by able to: explaining how to read scale drawings. 1. Convert measurements from one unit of measure to another. KEY TERMS 2. Identify common acute angle less than 90° measurement tools and angle two straight lines with a common end point or vertex, measured their uses. in degrees 3. Use measurement tools conversion factor number by which a measurement is multiplied or divided to change it to the same value in a different unit of measure to measure lines and angles. 1 degree (°) unit of measure of an angle, 360 of a circle 4. Accurately read linear measurement finding the length of lines or distance measurements in scale meter basic unit of linear measure in the metric system drawings. micrometer high precision measuring tool minute ( ) 1 of a degree ' 60 obtuse angle greater than 90° order of operations the sequence in which arithmetic operations are performed when more than one is required to solve a problem protractor instrument used to measure angles right angle 90° angle ruler straight edge marked in units of measure scale divisions on a measuring tool scale drawing presents an object in its exact shape but larger or smaller 1 second (") 60 of a minute tolerance acceptable range of precision in measurement upper and lower limit (±) measures plus or minus tolerance for a given figure, represents the limits of acceptable variation vernier caliper slide caliper with a short, graduated scale that slides along a longer, graduated instrument and is used to indicate fractional parts of divisions vertex point where the lines of an angle meet 169 1 Units of Measure Units of measurement have existed for thousands of years. The earliest units of measure were based on body parts. Ancient Egyptians measured length in “cubits,” the distance from the elbow to the fingertips, and in “hands,” a measurement still in use today to describe the height of horses. The English “foot” was originally the length of the foot of the king; an “inch” was the width of his thumb. A “rod,” which is equal to 16.5 feet, is a unit of measure used by surveyors. According to folklore, the rod was defined by measuring the combined length of the left feet of the first 16 men to walk out of church one Sunday morning. “Fathoms,” which is a measure of the depth of water, originated from the Anglo-Saxon word for “embrace.” A fathom was the distance between the outstretched arms of a man. UBC members working in the United States and Canada will need to work with linear measurements, the measurement of lines or distance in inches, feet, and yards and also in metric units of measure: millime- ters, centimeters, decimeters, and meters. Some jobs also involve the mea- surement of angles. Units of measure used with angles include degrees, minutes, and seconds. Although miles and kilometers are also commonly used units of measure, they are not often used in UBC trades and are not discussed in this chapter. Converting Between Inches, Feet, and Yards Inches, feet, and yards are English units of measure that came to Canada and the United States with the early English colonists. They describe dis- tance. Twelve inches equal one foot. Three feet equal one yard. Five thou- sand two hundred and eighty feet equal one mile. Figure 1 illustrates the relationship of inches, feet, and yards to each other. The examples also show the common abbreviations for inches, feet, and yards. Inches, feet, and yards can all be divided into fractional parts. The most commonly used fractional parts are halves, fourths, eighths, and sixteenths and also tenths and hundredths. The steel scale shown in Figure 2 subdi- vides each inch into halves, fourths, eighths, sixteenths, thirty-seconds, and sixty-fourths. Figure 3 shows another steel scale that has inches subdivided into hundredths along one edge. FIGURE 1 1inch 1 foot = 12 inches Relationship of inches, feet, and yards Abbreviations: 1 in., 1˝ Abbreviations: 1 ft., 1´ 1 yard = 3 feet = 36 inches Abbreviation: 1 yd. 170 Math for the Trades FIGURE 2 1 FIGURE 2 Fractional parts of an inch 64 1 64 1 32 1 16 1 8 1 4 1 2 1 FIGURE 3 Steel scale with inches in hundredths Converting Measurements From One Unit of Measure to Another On the job, it may be necessary to convert measurements from one unit of mea- sure to another. That process requires a conversion factor, a number by which the existing unit of measure is multiplied or divided to express the same value in a different unit of measure. Conversion factors are based on the relationship of the two units of measure to each other. For example, there are 12 inches in a foot. Twelve is the conversion factor for feet and MEASUREMENT inches. To convert feet to inches, multiply the number of feet by 12. To con- vert inches to feet, divide the number of inches by 12. Figure 4 illustrates how 32˝ can be converted to 2´-8˝. Table 1 lists conversion factors for feet, inches, and yards. 12 inches = 1 foot FIGURE 4 Conversion factor example 1 ft.2 ft.2 ft. 8 in. or 32 in. Measurement and Measurement Tools 171 TABLE 1 Conversion chart for feet, inches, and yards To convert Do this Feet to inches Multiply by 12 Inches to feet Divide by 12 Feet to yards Divide by 3 Yards to feet Multiply by 3 Yards to inches Multiply by 36 Inches to yards Divide by 36 Example 1 To convert inches to feet, find the number of feet in that number of inches. How many feet is 32 inches? Step 1: To convert 32 inches to feet, divide 32 by 12. 2 R 8 12 ⎠ 32 24 8 32 inches × 1 foot = 2.67 feet 12 inches Step 2: The equation is 32 ÷ 12 = 2 with a remainder of 8. Step 3: The result can be expressed in three ways. FIGURE 5 a) 32 in. = 2 ft. 8 in. Window dimensions for side b) 32 in. = 2 8 ft. which reduced to lowest terms is 2 2 ft. and top trim 12 3 3´-0˝ c) 32 in. = 2.67 ft. 3˝ Different Approaches to Conversion Problems On the job, converting measurements from one unit of measure to another may be just one part of a multi-part problem. For example, how many linear inches of 3˝ wide trim are needed to go around both sides and the top of the window in Figure 5? The diagram shows the dimensions: the height is 4´-5˝, and the width of the 4´-5˝ 4´-8˝ top is 2´-6˝. The width of the trim, 3˝, needs to be added to the dimensions of the window, making the height 4´-8˝ and the width 3´. Remember to include both sides of the window trim in the calculations. There are several ways to solve this problem. Example 1 demon- strates converting all of the measurements to inches and then add- 2´-6˝ ing the inches together to find the amount of trim needed. Example 3˝ 3˝ 2 adds the existing measurements together and then converts the 172 Math for the Trades sum to inches. Example 3 shows how to add measure- ment using decimal feet, and Example 4 shows how to do the whole calculation with one equation. Example 1 Adding inches. The first step is to separate the measurement 4´-8˝ into feet and inch components. Then multiply the number of feet (4´) by the correct conversion factor, in this case 12˝. The result is 48˝. Step 2 is to add the 48˝ back to the original 8˝ component. 4´-8˝ Step 1: 4 ft. × 12 in. = 48˝ 1 ft. Step 2: 48˝ + 8˝ = 56˝ Remember that there are two sides of trim. 56˝ × 2 = 112˝. Step 3: Convert the top trim from feet to inches. 3 ft. × 12 in. = 36˝ 1 ft. Step 4: Add the sides to the top 36˝ + 112˝ = 148˝ total trim required. Example 2 Adding feet and inches. Add all the inches together. Add all of the feet together. If the inch total is greater than 12, simplify. Step 1: Add the inches. 4´-8˝ side 4´-8˝ side 3´-0˝ top 16˝ Step 2: Add the feet. 4´-8˝ side MEASUREMENT 4´-8˝ side 3´-0˝ top 11´-16˝ Step 3: Simplify. 11´-16˝ = 12´-4˝ total trim required Example 3 Using decimal feet to make the calculation in one equation. Separate the measurement into its feet and inch components. Convert the inch component to a decimal of a foot and add to the feet. Add the measurements together. Measurement and Measurement Tools 173 TRADE TIP Step 1: 4´ component An easy way to remember 8˝ component mathematical order of Step 2: Convert 8˝ component to a decimal of a foot operations is this: 8 P = Please parentheses 12 = 12⎠ 8.0 = .67 E = Excuse exponent Add the decimal component back to the feet component M = My multiply D = Dear divide 4´ + .67´ = 4.67´ A = Aunt add Step 3: Add the lengths of all the pieces of trim together.