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

Copyright © Cengage Learning. All rights reserved. Unit 1C Review of Operations with Decimal Fractions and Percent

Copyright © Cengage Learning. All rights reserved. Addition and Subtraction of Decimal Fractions 1.10

4 Introduction to Decimals

5 A fraction whose denominator is 10, 100, 1000, or any power of 10 is called a decimal fraction. Decimal calculations and measuring instruments calibrated in decimals are the basic tools for measurement in the metric system. The common use of the calculator makes a basic understanding of decimal principles necessary.

6 Introduction to Decimals We know that the place values of the digits of a whole number. Each digit to the left of the decimal point represents a multiple of a power of 10. Each digit to the right of the decimal point represents a multiple of a power of

7 Introduction to Decimals Study Table 1.2, which shows place values for decimals. Note that 10 0 = 1. Table 1.2 Place Values for Decimals

8 Example 1 In the number , find the place value of each digit and the number it represents. We know that place values to the left of the decimal point are powers of 10 and place values to the right of the decimal point are powers of

9 Introduction to Decimals Often, common fractions are easier to use if they are expressed as decimal equivalents. Every common fraction can be expressed as a decimal. A repeating decimal is one in which a digit or a group of digits repeats again and again; it may be written as a common fraction. A bar over a digit or group of digits means that this digit or group of digits is repeated without ending.

10 Introduction to Decimals Each of the following numbers is a repeating decimal: is written is written is written is written A terminating decimal is a decimal number with a given number of digits. Examples are 0.75, , and

11 Introduction to Decimals Changing a Common Fraction to a Decimal To change a common fraction to a decimal, divide the numerator of the fraction by the denominator.

12 Example 4 Change to a decimal. (a terminating decimal) Divide the numerator by the denominator.

13 Introduction to Decimals Since a decimal fraction can be written as a common fraction with a denominator that is a power of 10, it is easy to change a decimal fraction to a common fraction. Simply use the digits that appear to the right of the decimal point (disregarding beginning zeros) as the numerator. Use the place value of the last digit as the denominator. Any digits to the left of the decimal point will be the whole-number part of the resulting mixed number.

14 Introduction to Decimals In on-the-job situations, it is often more convenient to add, subtract, multiply, and divide measurements that are in decimal form rather than in fractional form. Except for the placement of the decimal point, the four arithmetic operations are the same for decimal fractions as they are for whole numbers.

15 Introduction to Decimals Adding or Subtracting Decimal Fractions Step 1: Write the decimals so that the digits having the same place value are in vertical columns. (Make certain that the decimal points are also lined up vertically.) Step 2: Add or subtract as with whole numbers. Step 3: Place the decimal point between the ones digit and the tenths digit of the sum or the difference. (Be certain the decimal point is in the same vertical line as the other decimal points.)

16 Example 10 Perform the indicated operations: 51.6 – – difference sum final difference