Copyright © Cengage Learning. All rights reserved. Functions 3 The Metric System

Copyright © Cengage Learning. All rights reserved. Length 3.2

3 Length The basic SI unit of length is the metre (m). The height of a door knob is about 1 m. (See Figure 3.1.) One metre is a little more than 1 yd. (See Figure 3.2.) The height of a doorknob is about 1 m. One metre is a little more than 1 yd. Figure 3.1 Figure 3.2

4 Length Long distances are measured in kilometres (km) (1 km = 1000 m). The length of five city blocks is about 1 km. (See Figure 3.3.) The length of five city blocks is about 1 km. Figure 3.3

5 Length The centimetre (cm) is used to measure short distances, such as the width of the page (about 21 cm), or the width of a board. The width of your small fingernail is about 1 cm. (See Figure 3.4.) The width of your small fingernail is about 1 cm. Figure 3.4

6 Length The millimetre (mm) is used to measure very small lengths, such as the thickness of a sheet of metal or the depth of a tire tread. The thickness of a dime is about 1 mm. (See Figure 3.5.) The thickness of a dime is about 1 mm. Figure 3.5

7 Length Each of the large numbered divisions on the metric ruler in Figure 3.6 marks one centimetre (cm). The smaller lines indicate halves of centimetres, and the smallest divisions show tenths of centimetres, or millimetres. Metric ruler Figure 3.6

8 Example 1 Read A, B, C, and D on the metric ruler in Figure 3.7. Give each result in millimetres, centimetres, and metres. Answers: A = 12 mm, 1.2 cm, m B = 20 mm, 2.0 cm, m C = 25 mm, 2.5 cm, m D = 128 mm, 12.8 cm, m Figure 3.7

9 Length Choosing Conversion Factors The correct choice for a given conversion factor is the one in which the old units are in the numerator of the original expression and in the denominator of the conversion factor, or the old units are in the denominator of the original expression and in the numerator of the conversion factor. That is, set up the conversion factor so that the old units cancel each other.

10 Example 2 Change 3.6 km to metres. Since kilo means 10 3 or 1000, 1 km = 1000 m. The two possible conversion factors are and Choose the one whose numerator is expressed in the new units (m) and whose denominator is expressed in the old units (km). This is conversion factor