1.04 The real number system
Consider the folllowing sets of numbers:
Identify the set of all integers.
Identify the set of whole numbers.
Identify the smallest whole number.
\left\{0, 1, 2, 3, \ldots\right\}
\left\{\ldots, - 3 , - 2 , - 1 , 0, 1, 2, 3, \ldots\right\}
\left\{1, 2, 3, \ldots\right\}
\left\{\ldots, - 3 , - 2 , - 1 , 0\right\}
Classify the set of numbers containing \left\{0, 1, 2, \ldots\right\}
Consider the following diagram:
Determine whether each of the following statements is true or false:
\sqrt{13} is a rational number.
When written in decimal form, irrational numbers have a repeating pattern of decimal digits.
A real number is either a rational or irrational number.
Classify the following numbers:
Can a number be both rational and irrational? Explain your answer.
Every whole number is also a rational number but not every rational number is a whole number. Explain why this statement is true.
Christa decides to express her favorite rational number as a decimal. Could the decimal be repeating, terminating or either?
Akin states that 24.737337333... is a rational number because it has a repeating pattern.
Is Akin correct? Explain your answer.
State whether each of the following numbers are rational or irrational:
-\dfrac{2}{7}
\sqrt{2}
8
20.57
3\sqrt{5}
1-\sqrt{7}
-0.\overline{3}
\pi
Simplify each of the following numbers and state whether they are rational or irrational:
\sqrt{16}
\dfrac{2\pi}{8}
-\dfrac{4\pi}{5\pi}
\dfrac{0.4}{5}
State the set of numbers most appropriate to describe the following:
The populations of towns.
The times of the runners (in seconds) in a 100\text{ m} sprint.
Distance between Jupiter and Venus.
The position of a submarine relative to sea level. (Note that height above sea level is expressed as a positive quantity.)
The goal difference of a hockey team at the end of a season. (Note that the goal difference is the number of goals the team scored in the season minus the number of goals that were scored against them.)
The cost (in dollars) of sending a text message.
The circumference of a circle is given by 2 \pi r, where r is the radius.
State whether each of the following statements is true:
The circumference is an irrational number if the radius is rational.
The circumference is a rational number if the radius is equal to \pi.
The circumference is a rational number if the radius is irrational.
The circumference is a rational number if the radius is equal to \dfrac{a}{\pi} where a is an integer.