Decimals and Rational Numbers Overview
Dive into the world of decimals and rational numbers through this detailed presentation, covering topics such as converting rational numbers to decimals, understanding terminating and repeating decimals, practical examples, and skill checks. Explore how to express rational numbers as decimals and handle fractions with denominators that are not powers of 10. Master the conversion process with step-by-step guidance and visual aids.
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CHAPTER 5 Section 5.5 Decimals and Rational Numbers FoM PPT Template1.jpg FoM PPT Template1.jpg Book cover image by iStock.com/McKevin Shaughnessy
Section 5.5 p. 220 Rational numbers have decimal equivalents. A decimal form of a rational number will be either a terminating or repeating decimal. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 220 When the denominator of a rational number is a power of 10, converting the rational number to decimal form is easy. When the denominator is not a power of 10, try renaming the rational number as an equivalent fraction with a denominator that is a power of 10. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 220 Example 1 Change the following rational numbers to decimals. 2 5 2 2 5 2 a. 4 2 5 = = 0.4 = 10 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 220 Example 1 Change the following rational numbers to decimals. 152 25 152 25 100 b. 152 4 25 4 =608 = = 6.08 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 221 Skill Check 1 Express each rational number as a decimal. 2. 48 137 20 7 1. 3. 5 10 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 221 Skill Check 1 Express each rational number as a decimal. 5. 164 4. 11 500 25 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 221 If it is difficult or impossible to write a fraction with a denominator that is a power of 10, you can divide the numerator by the denominator. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 221 Example 2 0.3 7 5 Change the following rational numbers to decimals. 3 8 8 3.000 2 4 60 56 a. = 0.375 40 40 The decimal terminates. 0 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 221 Example 2 0.3 3 3 Change the following rational numbers to decimals. 1 3 3 1.000 9 10 b. = 0.333 = 0.3 9 10 The decimal repeats. 9 1 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Example 3 0.2 7 2 3 11 Write the rational number as a decimal. 3 11 11 3.000 2 2 80 77 = 0.272 = 0.27 30 22 The decimal repeats. 8 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Skill Check 2 Express the following rational numbers as decimals. 1. 5 16 2. 2 9 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Skill Check 2 Express the following rational numbers as decimals. 3. 5 12 4. 15 8 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 To write a terminating decimal in rational form, the decimal part is placed in the numerator, and the denominator is the power of 10 that corresponds to the place value of the last digit. Remember to express fractions in lowest terms. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Example 4 Express each as a rational number in lowest terms. 24 100 100 4 24 4 6 a. 0.24 = = = 25 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Example 4 Express each as a rational number in lowest terms. 375 1,000 1,000 475 25 200 25 2,375 5 1,000 5 19 8 475 200 = 2,375 b. 2.375 = 2 = = = = FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Skill Check 3 Express each as a rational number. 2. 0.47 1. 0.6 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 Skill Check 3 Express each as a rational number. 4. 7.125 3. 23.75 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 All rational numbers can be expressed as either terminating or repeating decimals. However, not all decimals are rational numbers. Non-repeating, non-terminating decimals are irrational numbers. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 222 = 3.141592654 2 = 1.414213562 2.020020002 0.123456789101112131415161718192021 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 223 Skill Check 4 Classify each decimal as terminating, repeating, or irrational. Use a bar to simplify any repeating decimals. 1. 0.454545 2. 0.54166666 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 223 Skill Check 4 Classify each decimal as terminating, repeating, or irrational. Use a bar to simplify any repeating decimals. 3. 0.583 4. 2.121121112 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 223 Skill Check 4 Identify each number as rational or irrational. 5. 0.5838383 6. 0.929229222 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 223 Skill Check 4 Identify each number as rational or irrational. 7. 15 8. 0.541666 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 223 Example 5 7 15 Compare 0.4 and by comparing their decimal equivalents. 0.46 Since 0.4 < 0.46, 15 7.000 7 0.4 < 15 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.5 p. 224 Skill Check 5 Compare these rational numbers by comparing their decimal forms. 7 11 36 57 15 8 32 17 1. 2. , , FoM PPT Template1.jpg FoM PPT Template1.jpg
