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Exercises Expressions, exponents and radicals

Example 7.2 from Prealgebra, 7.1 Rational and Irrational Numbers

Rational and Irrational Numbers: example 7.2

Identify each of the following as rational or irrational:

ⓐ $0.58 \overset{–}{3}$
ⓑ $0.475$
ⓒ $3.605551275…$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
ⓐ $0.58 \overset{–}{3}$
The bar above the $3$ indicates that it repeats. Therefore, $0.58 \overset{–}{3}$ is a repeating decimal, and is therefore a rational number.
ⓑ $0.475$
This decimal stops after the $5$ , so it is a rational number.
ⓒ $3.605551275…$
The ellipsis $(…)$ means that this number does not stop. There is no repeating pattern of digits. Since the number doesn't stop and doesn't repeat, it is irrational.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Identify each of the following as rational or irrational:

ⓐ $0.29$ ⓑ $0.81 \overset{–}{6}$ ⓒ $2.515115111…$

How did it go?

PreviousRational and Irrational Numbers: example 7.1 Next Rational and Irrational Numbers: example 7.3

From Prealgebra (1st edition) by OpenStax (Rice University), section 7.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.