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Chapter 5: Problem 10

Give an example of a number that is a rational number, an integer, and a real number.

Short Answer

Expert verified
A number that satisfies the conditions of being a rational number, an integer, and a real number is 2.

Step by step solution

01

Understand the Terms

First of all, look at the definitions of rational numbers, integers, and real numbers. Rational numbers are numbers that can be written as the ratio of two integers. Integers are any whole numbers, positive or negative, including zero. Real numbers is a set that includes all rational and irrational numbers.
02

Identify a number that satisfies all three

Remember that integers are a subset of rational numbers (as we can express an integer as the ratio of itself to 1, and rational numbers are a subset of real numbers as they can be expressed as decimal points). This means every integer is both a rational number and a real number by definition.
03

Select a number

Select any integer, for instance, 2. It should satisfy all three conditions being an integer, a rational number (which can be written as 2/1), and a real number.
04

Confirm the Satisfaction of All Conditions

Finally, confirm that the selected number (2, in this case) satisfies all the conditions of being a rational number (since 2 can be expressed as 2/1), an integer (since 2 is a whole number), and a real number (since all integers and fractions are considered real numbers).

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Most popular questions from this chapter

You will develop geometric sequences that model the population growth for California and Texas, the two most populated U.S. states. The table shows the population of Texas for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 20.85 & 21.27 & 21.70 & 22.13 & 22.57 & 23.02 \\ \hline \end{array} $$ $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 23.48 & 23.95 & 24.43 & 24.92 & 25.15 \\ \hline \end{array} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that Texas has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling Texas's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project Texas's population, in millions, for the year 2020 . Round to two decimal places.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=20, r=-4\)

The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(7,19,31,43, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=3\)

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(3,15,75,375, \ldots\)
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