PRACTICE Irrational vs Rational Numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Examples include 1/2, 3, and -4.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction. It cannot be written as \( \frac{a}{b} \) where \( a \) and \( b \) are integers. Examples include \( \pi \) and \( \sqrt{2} \).

Front

Which of the following is a rational number: \( \sqrt{127} \), \( \pi \), 2.5, or 8.98763...?

Back

2.5 is a rational number because it can be expressed as \( \frac{25}{10} \) or \( \frac{5}{2} \).

Front

Is \( \sqrt{81} \) rational or irrational?

Back

Rational, because \( \sqrt{81} = 9 \), which is an integer.

Front

What is \( \sqrt{36} \)?

Back

6, because \( 6 \times 6 = 36 \).

Front

What is \( \sqrt{64} \)?

Back

8, because \( 8 \times 8 = 64 \).

Front

Is the number 0.4444444... rational or irrational?

Back

Rational, because it can be expressed as \( \frac{4}{9} \).

Front

What is the decimal representation of \( \frac{1}{4} \)?

Back

0.25, which is a rational number.

Front

What is the square root of a perfect square?

Back

The square root of a perfect square is always a rational number. For example, \( \sqrt{25} = 5 \).

Front

Can a repeating decimal be a rational number?

Back

Yes, a repeating decimal can be expressed as a fraction, making it a rational number. For example, 0.333... is \( \frac{1}{3} \).