Practice Solutions

Determine if the number is rational or irrational. Explain.

$7.251683 . . . .$

Irrational. The decimal is non-repeating, non-terminating

$\frac{3}{8}$

Rational. It is a ratio of two integers 3 and 8

$- \frac{7}{7}$

Rational. It is a ratio of two integers –7 and 7

$π$

$π = 3.141592654 . . .$

Irrational. When written as a decimal, it is non-repeating, non-terminating.

For problems 5–12, classify the given number into all sets of real numbers to which it belongs, then place the number in the most specific number set in the diagram.

$\frac{18}{3}$

$\frac{18}{3} = 6$

Natural, Whole, Integer, Rational, Real

$\sqrt{5}$

$\sqrt{5} = 2.236067977 . . .$

Irrational, Real

$\frac{8}{9}$

Rational, Real

$- \frac{16}{4}$

$- \frac{16}{4} = - 4$

Integer, Rational, Real

$\sqrt{100}$

$\sqrt{100} = 10$

Natural, Whole, Integer, Rational, Real

Whole, Integer, Rational, Real

$125 %$

$125 % = 1.25$

Rational, Real

2.717273747…

Irrational, Real