Rational and Irrational Numbers

Rational and Irrational Number Review

Rational Numbers

• A rational number is a number that can be written as a fraction. This includes:

• Whole numbers    $2,\ -3,\ 102$  

• Fractions    $\frac{1}{2},\ -\frac{3}{4}$  

• Decimals that end    $2.5,\ -0.5$ 

• Decimals that go on with a repeating pattern    $0.333...,\ \ -1.414141...$  

• Square/cube roots that we know the exact values    $\sqrt{25},\ -\sqrt{36},\ \ ^3\sqrt{8}$  

Irrational Numbers

• An irrational number is a number that can not be written as a fraction. This includes:

• Decimals that go on without a repeating pattern

   $2.13478...,\ -1.25734...$  

• Square/cube roots that we do not know the exact values    $\sqrt{66},\ \ ^3\sqrt{23}$  

Multiple Choice

Which of the following is a rational number?

• $$\frac{5}{6}$$

• $$\sqrt{68}$$

• $$1.14624...$$

• $$\sqrt{101}$$

Multiple Choice

Which of the following is a rational number?

• $$\sqrt{52}$$

• $$\sqrt{68}$$

• $$\sqrt{100}$$

• $$\sqrt{101}$$

Multiple Choice

Which of the following is an irrational number?

• $$0.3$$

• $$\sqrt{8}$$

• $$\sqrt{49}$$

• $$\frac{5}{22}$$

Multiple Choice

Which of the following is an irrational number?

• $$6$$

• $$\sqrt{81}$$

• $$-1.2$$

• These are all rational

Multiple Choice

Is the cube root of 3 rational or irrational? 

• rational

• irrational

Multiple Choice

Is the cube root of 125 rational or irrational? 

• rational

• irrational

Multiple Choice

What type of number is a fraction?

• rational

• irrational

Multiple Choice

What type of number is a decimal that repeats with a pattern forever?

• rational

• irrational

Multiple Choice

What type of number is a square root that we can only estimate?

• rational

• irrational

Multiple Choice

Between what two whole numbers is $$\sqrt{6}$$ ?

• 1 and 2

• 2 and 3

• 3 and 4

• 4 and 5

Multiple Choice

Between what two whole numbers is $$\sqrt{35}$$ ?

• 2 and 3

• 3 and 4

• 4 and 5

• 5 and 6

Multiple Choice

Between what two whole numbers is the cube root of 10?

• 2 and 3

• 3 and 4

• 4 and 5

• 5 and 6

Multiple Choice

Between what two whole numbers is the cube root of 52?

• 2 and 3

• 3 and 4

• 4 and 5

• 5 and 6