1.Number System Quiz

What is the definition of a rational number?

• A number that is not a real number

• A number that is not a whole number

• A number that cannot be expressed as a fraction

• A number that can be expressed as the quotient or fraction of two integers

Is the number 3.14 a rational number? Why or why not?

• No

• Yes, because it can be expressed as a fraction

• No, because it is a whole number

• Yes, because it is a repeating decimal

If a and b are both integers, can a/b be a rational number? Explain.

• Yes

• No, because a/b will always be an imaginary number

• No, because a/b will always be a complex number

• No, because a/b will always be an irrational number

What is the decimal representation of the rational number 2/5?

• 0.2

• 0.6

• 0.8

• 0.4

Is the square root of 16 a rational number? Why or why not?

• Yes

• No, because the square root of 16 is a fraction

• No, because the square root of 16 is a whole number

• No, because the square root of 16 is an irrational number

What is the definition of an irrational number?

• A rational number

• A whole number

• A real number that cannot be expressed as a ratio of two integers.

• A prime number

Give an example of an irrational number.

• 100

• √2 (square root of 2)

• 3.14

• 1/2

Is the number 0.333... an irrational number? Why or why not?

• No, because it is a terminating decimal

• No, because it can be expressed as a fraction

• No, because it is a repeating decimal

• Yes

Can the sum of a rational number and an irrational number be rational? Explain.

• Yes

• No, because rational numbers can only be added to other rational numbers

• No, because the sum of any rational and irrational number is always irrational

• No, because all irrational numbers are also real numbers

Explain why the number pi (π) is an irrational number.

• The number pi (π) is an irrational number because its decimal representation is finite

• The number pi (π) is an irrational number because it can be expressed as a simple fraction

• The number pi (π) is an irrational number because it cannot be expressed as a simple fraction and its decimal representation goes on infinitely without repeating.

• The number pi (π) is an irrational number because it is a whole number