Understanding Rational and Irrational Numbers

What is a rational number?

• A number that can be written as a fraction of two integers.

• A number that can be written as a fraction of any two numbers.

• A number that is always a whole number.

• A number that has a decimal form that never terminates or repeats.

Which of the following statements about integers and rational numbers is true?

• All integers are rational numbers.

• All rational numbers are integers.

• Integers include decimals and fractions.

• The denominator of a rational number can be zero.

Is 2.75 a rational number?

• No, because it is a decimal.

• Yes, because it is a terminating decimal.

• No, because it cannot be written as a fraction.

• Yes, because it is a repeating decimal.

Is 0.333... (0.3 repeating) a rational number?

• No, because it is a non-terminating decimal.

• Yes, because it is a repeating decimal.

• No, because it cannot be written as a fraction of two integers.

• Yes, because it is an integer.

Which of the following decimal numbers is rational?

• A decimal with an infinite number of non-repeating digits

• A decimal that terminates

• A non-repeating, non-terminating decimal

• A decimal that neither terminates nor repeats

Which of the following numbers is a rational number?

• √3

• π

• 0.121221222...

• 7/8

Which of the following numbers is an irrational number?

• √49

• 0.333...

• -5

• √10

What is a defining characteristic of an irrational number?

• It can be written as a fraction of two integers.

• Its decimal representation terminates.

• Its decimal representation repeats in a pattern.

• Its decimal representation neither terminates nor repeats.

Why is the square root of 2 considered an irrational number?

• It can be expressed as a simple fraction like 2/1.

• Its decimal form is exactly 1.414.

• Its decimal representation goes on forever without repeating.

• It is a negative number.

Which of the following numbers is an irrational number?

• -63

• The square root of 49

• 8.71425 with a bar over 71425

• The square root of 50