determining rational and irrational 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 \( b \neq 0 \).

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.

Front

Classify the number \( \frac{\pi}{2} \).

Back

Irrational

Front

Classify the number \( \frac{3}{5} \).

Back

Rational

Front

Are terminating decimals rational?

Back

Always

Front

Which of the following is a rational number: \( \pi \), \( \sqrt{8} \), 0.56565656..., \( \sqrt{10} \)?

Back

0.56565656... (it is a repeating decimal).

Front

Which of the following is rational: 0.211232112421125..., \( \pi \), \( \sqrt{25} \), \( \sqrt{12} \)?

Back

\( \sqrt{25} \) (it equals 5, which is a whole number).

Front

What is a terminating decimal?

Back

A terminating decimal is a decimal number that has a finite number of digits after the decimal point.

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal number that has one or more digits that repeat infinitely.

Front

Is the square root of a perfect square rational or irrational?

Back

Rational (e.g., \( \sqrt{16} = 4 \)).