1.01 The real number system
Interactive practice questions
Using the diagram, determine whether the following statement is true or false:
$\sqrt{13}$√13 is a rational number.
At the top, a large rectangle is labeled "Real numbers" encompassing the entire set. Within this rectangle, there are two large subsets: the upper subset is shaded dark green and labeled "Rational numbers," and the lower subset is shaded blue and labeled "Irrational numbers." Within the upper subset is a blue-green rectangle labeled "Integers," and within it is a light-green rectangle labeled "Whole numbers."
The diagram shows the relationship between the sets of numbers. The set of real numbers includes the sets of rational and irrational numbers. The set of integers is a subset of the set of rational numbers. The set of whole numbers is a subset of the set integers, which in turn is also a subset of the set of rational numbers.
Examples of rational numbers, which include $-\frac{112}{17}$−11217, $-3.12$−3.12, $-\frac{3}{2}$−32, $\frac{1}{2}$12, $1.3$1.3, $2.\overline{6}$2.6,$\frac{13}{3}$133, are listed within the dark-green rectangle. Examples of irrational numbers, which include $\frac{-\sqrt{102}}{5}$−√1025 , $-\sqrt[3]{2}$−3√2, $\frac{1+\sqrt{5}}{2}$1+√52, $\pi$π and $\sqrt{21}$√21, are listed within in the blue rectangle. Examples of integers, which include the whole numbers, $-1$−1, $-2$−2, $-3$−3, and $-4$−4, are listed within the blue-green rectangle. Examples of whole numbers, which include $0$0, $1$1, $2$2, $3$3, $4$4, are listed within the light-green rectangle.
True
False
Using the diagram, determine whether the following statement is true or false:
When written in decimal form, irrational numbers have a repeating pattern of decimal digits.
Using the diagram, classify the number $38$38.
Select all that apply.
Using the diagram, classify the number $-42$−42.