Which of the following are rational numbers? -4,5 . 6, √(29), 0, π, 4.02, (7)/(9).

Name: Problem 3, Chapter 1: Beginning and Intermediate Algebra
Uploaded: 2021-03-17T21:30:09-08:00
Duration: 1 min 56 s
Channel: Julie Silva
Description: Which of the following are rational numbers? -4,5 . 6, √(29), 0, π, 4.02, (7)/(9).

step 1 What we're being asked to do is determine which of the following are rational numbers. Well, rem

Which of the following are rational numbers? -4,5 . 6,...

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Key Concepts

Rational Numbers

A rational number is defined as any number that can be expressed in the form a/b, where a and b are integers and b is not zero. This definition encompasses integers, as they can be written as the fraction of the number over 1, as well as decimals that either terminate or repeat.

Repeating and Terminating Decimals

Decimals that either come to an end (terminating) or have a repeating pattern (repeating decimals) are always rational numbers because they can be converted into a fraction form. The process of converting a repeating decimal to a fraction involves algebraic manipulation that represents the infinite repetition in a finite ratio of integers.

Irrational Numbers

Irrational numbers are those that cannot be written as a ratio of two integers. They have non-terminating, non-repeating decimal expansions. Common examples include numbers like ? and square roots of numbers that are not perfect squares, which cannot be exactly represented as fractions.

Square Roots

The square root of a number is rational if and only if the original number is a perfect square (like 4, 9, 16, etc.). When the number is not a perfect square, its square root is irrational, as it cannot be expressed as a simple fraction of two integers.

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