Copyright © Cengage Learning. All rights reserved. Functions 1 Basic Concepts

Copyright © Cengage Learning. All rights reserved. Unit 1B Review of Operations with Fractions

Copyright © Cengage Learning. All rights reserved. The U.S. System of Weights and Measures 1.9

4 The U.S. System of Weights and Measures Measurement is the comparison of an observed quantity with a standard unit quantity. A standard unit that is constant, accurate, and accepted by all is needed for technical measurements. The U.S. system of weights and measures, which is derived from and sometimes called the English system, is a combination of makeshift units of Anglo-Saxon, Roman, and French-Norman weights and measures.

5 The U.S. System of Weights and Measures The metric system, which is now used by international industry and business, all major U.S. industries, and most federal agencies. The U.S. system requires us to understand and be able to use fractions in everyday life. One advantage of the metric system is that the importance of fractional computations is greatly reduced.

6 Example 1 Change 5 ft 9 in. to inches. 1 ft = 12 in., so 5 ft = 5  12 in. = 60 in. 5 ft 9 in. = 60 in. + 9 in. = 69 in.

7 The U.S. System of Weights and Measures To change from one unit or set of units to another, we use what is commonly called a conversion factor. We know that we can multiply any number or quantity by 1 (one) without changing its value. We also know that any fraction whose numerator and denominator are the same is equal to 1.

8 The U.S. System of Weights and Measures For example,,, and. Also, since 12 in. = 1 ft,, and likewise,, because the numerator equals the denominator. We call such names for 1 conversion factors (or unit conversion factors).

9 The U.S. System of Weights and Measures 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. The use of a conversion factor is especially helpful for units with which you are unfamiliar, such as rods, chains, or fathoms.