Rational vs. Irrational Numbers

Which of the following is an example of a rational number between 7 and 8?

• 7.8333333...

• √52

• 7 1/9

• Both a and c

• All of the above

Answer explanation

The rational numbers between 7 and 8 are 7.8333333... and 7 1/9. Therefore, both choices a and c are examples of rational numbers between 7 and 8.

Tags

CCSS.8.NS.A.2

Which of the following is an example of an irrational number between 6 and 7?

• 2π

• 6.875

• √32

• Both a and c

• All of the above

Answer explanation

The correct choice is 2π, which is an irrational number between 6 and 7 as it is approximately 6.28, falling within the given range.

Tags

CCSS.8.NS.A.1

The square roots of perfect squares will ________ be irrational numbers.

• sometimes

• always

• never

• frequently

Repeating decimals will ________ be rational numbers.

• sometimes

• always

• never

• frequently

Tags

CCSS.8.NS.A.1

CCSS.7.NS.A.2D

Square roots will ________ be irrational numbers.

• sometimes

• always

• never

• frequently

Answer explanation

Square roots can be rational (e.g., the square root of 4 is 2) or irrational (e.g., the square root of 2). Therefore, square roots will sometimes be irrational numbers.

Tags

CCSS.8.NS.A.1

Liam is measuring the temperature in his science experiment. Which is an example of a rational value between -8 and -9 degrees Celsius?

• -8.5

• -√100

• -7.75

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

• rational

• irrational

• rational

• irrational

Tags

CCSS.8.NS.A.1

Rational or Irrational?

0.15893...

• rational

• irrational

Answer explanation

The number 0.15893... is irrational because it is a non-repeating and non-terminating decimal, which cannot be expressed as a ratio of two integers.

Tags

CCSS.8.NS.A.1

CCSS.7.NS.A.2D

Rational or Irrational?

-17

• rational

• irrational

Answer explanation

The number -17 is a rational number because it can be expressed as a ratio of two integers (-17/1). Rational numbers are those that can be written as a fraction.