Consider the folllowing sets of numbers.
Write the set of all integers, \Z.
Write the set of whole numbers.
State the smallest whole number.
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:
Every whole number is also a rational number but not every rational number is a whole number. Explain why this statement is true.
Christa wants to express her favorite rational number as a decimal. Determine if the number could be a terminating decimal, a repeating decimal, or either.
State the set of numbers most appropriate to describe each of the following, and explain your choice:
The population of a town.
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.
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.
Write a definition for the subset of rational numbers.
Write a definition for the subset of irrational numbers.
Can a number be both rational and irrational? Explain your answer.
Akin states that 24.737\,337\,333... is a rational number because it has a repeating pattern.
Is Akin correct? Explain your answer.
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 about the circumference of the circle.
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.