The Real Number System

Front

What is the definition of a rational number?

Back

A rational number is any number that can be expressed as a fraction, where both the numerator and the denominator are integers and the denominator is not zero.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a fraction of two integers.

Front

Are all square roots irrational numbers?

Back

No, not all square roots are irrational. For example, the square root of 4 is 2, which is a rational number.

Front

What is an example of a rational number that is not a whole or natural number?

Back

3.14 is an example of a rational number that is not a whole or natural number.

Front

Can fractions be irrational numbers?

Back

No, fractions are rational numbers as long as they can be expressed as a ratio of two integers.

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal fraction that eventually repeats the same sequence of digits indefinitely.

Front

Are repeating decimals considered rational numbers?

Back

Yes, repeating decimals are examples of rational numbers.

Front

What is the difference between whole numbers and natural numbers?

Back

Natural numbers are the set of positive integers (1, 2, 3, ...), while whole numbers include all natural numbers plus zero (0, 1, 2, 3, ...).

Front

What is the decimal representation of the rational number 1/3?

Back

The decimal representation of 1/3 is 0.333..., which is a repeating decimal.

Front

Is the number 0.5 a rational number?

Back

Yes, 0.5 is a rational number because it can be expressed as the fraction 1/2.