224 CHAPTER 5 Number Theory and the Real Number System In Sections 1.1 and 5.1, we defined the natural or counting numbers: N {1, 2, 3, 4, } = … As the natural numbers get larger, we use words such as thousand, million, billion, trillion, etc. to help pronounce these large numbers. To help understand when to use these words, look at the following diagram of the number 123,456,789,123,456. 123, 456, 789, 123, 456 trillion billion million thousand In spoken form, the number 123,456,789,123,456 is: one hundred twenty-three trillion, four hundred fifty-six billion, seven hundred eighty-nine million, one hundred twenty-three thousand, four hundred fifty-six. In our next example, we will practice writing large numbers given their spoken form. Answer the question, What is the temperature, to the nearest degree Fahrenheit, outside right now? Depending on where you are and what time of year it is, you may have answered with a positive number, a negative number, or zero. These numbers are examples of the group of numbers called the integers that we will study in this section. We will also study the operations of addition, subtraction, multiplication, and division using the integers. The Integers SECTION 5.2 LEARNING GOALS Upon completion of this section, you will be able to: 7 Add integers. 7 Subtract integers. 7 Multiply integers. 7 Divide integers. 7 Simplify expressions involving exponents on integers. 7 Simplify expressions using the order of operations. Why This Is Important We all use integers daily. An understanding of the integers and their properties is important to successfully complete our everyday tasks. Applications we study in this section include elevation differences, temperature changes, and time zone calculations. Example 1 Writing Large Natural Numbers Write the natural number given in its spoken form. a) Four hundred twenty-seven million, three hundred sixty-five thousand, one hundred eighty-nine b) Three trillion, forty-five billion, eight million, six c) Two hundred million d) Thirty-eight point six trillion e) Five point zero seven billion Solution Now try Exercise 5 a) 427,365,189 b) 3,045,008,000,006 c) 200,000,000 d) We can think of thirty-eight point six trillion as 38.6 trillion. This number can also be spoken as thirty-eight trillion, six hundred billion. Therefore, the written number is 38,600,000,000,000. e) We can think of five point zero seven billion as 5.07 billion. This number can also be spoken as five billion, 70 million. Therefore, the written number is 5,070,000,000. 7 Neyman Kseniya/Shutterstock
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