Rational and Irrational Number Review

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