Unit 6: Rational & Irrational Numbers Review

Real Number System

​https://www.youtube.com/watch?v=tC7NkH5xwBM

If rational numbers can be written as fractions, the irrational numbers cannot.

Multiple Choice

Is $$\frac{77}{3}$$  rational or irrational?

• Rational

• Irrational

Multiple Choice

Is $$.\overline{11}$$ rational or irrational?

• Rational

• Irrational

Multiple Choice

Is $$-\sqrt{64}$$  rational or irrational?

• Rational

• Irrational

Multiple Choice

Is $$\sqrt{40}$$  rational or irrational?

• Rational

• Irrational

Multiple Choice

Is $$17.33$$  rational or irrational?

• Rational

• Irrational

Multiple Choice

Select the ONLY irrational number:

• $$\frac{152}{6}$$

• $$.149203827...$$

• $$3\times\sqrt{4}$$

• $$-.747474747474...$$

Multiple Choice

Is $$-2\pi$$  rational or irrational?

• Rational

• Irrational

Multiple Choice

.141414141414...

• Rational 
• Irrational 

Multiple Choice

pi - 3.141592....

• Rational
• Irrational 

Multiple Choice

√25

• Rational
• Irrational

Multiple Choice

What is a rational number?

• A number that makes sense

• a number that can be written as a fraction of whole numbers

• any number you can enter into a calculator

• a number that has a square root

Multiple Choice

4π

• rational
• irrational

​Classiying Rational Numbers

Multiple Choice

Does the graphic organizer correctly group the numbers?

• Yes
• No

Multiple Choice

includes integers, fractions, terminating and repeating decimals.

• Rational Numbers
• Irrational Numbers

Multiple Choice

Classify the Number: -23

• Rational
• rational, integer
• integer
• rational, whole

Multiple Choice

How would 5/9 be classified?

• rational and real
• whole and integer
• only real
• only irrational

Multiple Choice

Square Root of 93

• Rational
• Natural
• Whole
• Irrational

Multiple Choice

Classify 17/10

• Whole
• Rational
• Natural
• None of the above

Multiple Choice

Classify √35.

• Rational, Integer
• Whole, Integer, Rational 
• Irrational, Integer
• Irrational

Multiple Choice

What number below is a natural, whole, integer, rational, and real number ?

• -4
• 5.1
• 0.7
• 3

Multiple Select

Classify the number by checking all the boxes that apply.

-6.75

• Rational

• Irrational

• Integer

• Whole

• Natural/Counting

Multiple Select

Classify the number by checking all the boxes that apply.

$$\sqrt{25}$$  

• Rational

• Irrational

• Integer

• Whole

• Natural/Counting

Multiple Select

Classify the number by checking all the boxes that apply.

5π

• Rational

• Irrational

• Integer

• Whole

• Natural/Counting

Multiple Select

Classify the number by checking all the boxes that apply.

- $$\sqrt{9}$$  

• Rational

• Irrational

• Integer

• Whole

• Natural/Counting

Multiple Select

Classify the number by checking all the boxes that apply.

-2.5

• Rational

• Irrational

• Integer

• Whole

• Natural/Counting

​Converting fractions to decimals

​To Convert fraction to decimal simply divide.

Multiple Choice

What is 2/3 as a decimal?

• 2.3

• 0.66 (repeating)

• 3.2

• 6.6

Multiple Choice

Convert  2 $$\frac{3}{10}$$  to a decimal.

• 2.03

• 2.3

• 2.33

• 23.3

Multiple Choice

Convert the mixed number  $$1\frac{1}{6}$$ to a decimal .

• 1.6

• 1.67

• 0.1666

• $$1.1\overline{6}$$  

• 1.1

Multiple Choice

Convert to a decimal

2/11

• 0.1818...

• .2111...

• .1919...

• .18

Multiple Choice

Write 0.08 as a fraction

• 8/10
• 8/100
• 0/8
• 8/0

Multiple Choice

What does the fraction bar represent or translate to in a fraction?

• Under

• Multiply

• Divided by

• Denominator

Convert Terminating & Repeating decimals into fraction

​Use Desmos Calculator

Multiple Choice

Convert 0.30 into a fraction

• 1/3
• 2/5
• 4/10
• 3/10

Multiple Choice

Convert 0.75 into a fraction

• 3/4
• 2/3
• 4/5
• 1/2

Multiple Choice

Convert 0.252525... to a fraction.

• 25/9
• 25/99
• 25/100
• 1/4

Multiple Choice

Convert 0.769769769... to a fraction.

• 769/999
• 769/1000
• 769/100
• 769/99

Multiple Choice

• 77/25
• 77/250
• 308/9
• 308/999

Multiple Choice

• 2   23/100
• 2   23/10
• 2   23/9
• 2   23/99

Multiple Choice

In the decimal   .263,  the place value of
"6" is called the _____.

• tenths
• hundreds
• hundredths
• thousandths

Let's Review Exponents

Multiple Choice

2² = _____

• 2
• 6
• 4
• 16

Multiple Choice

What is the
product of 5² ?

• 52
• 10
• 25
• 100

Multiple Choice

Simplify 3³

• 6
• 33
• 9
• 27

Multiple Choice

 100¹ is the same as ...
 

• 100
• 1000
• 1
• 10

Multiple Choice

What is  0⁸²  equal to ? 

• 0
• 1
• 82
• 8200

Multiple Choice

 1⁹⁹  is equivalent to ...

• 99
• 1
• 0
• 199

Square root & Cube Root

Multiple Choice

The area of a square is 36 cm².  What is the length of one side?

• 6 cm
• 24 cm
• 9 cm
• 9 cm

Multiple Choice

√196 = ______

• 14
• 14²
• 15
• 15²

Multiple Choice

Solve √x = 10

• 100, -100
• -100
• 100

Multiple Choice

Solve √x = 25

• 5
• -5
• 625
• -625

Multiple Choice

Which of the following is irrational?

• $$\sqrt{49}$$

• $$\sqrt{50}$$

• $$\sqrt{81}$$

• $$\sqrt{121}$$

Multiple Choice

$$^{3\sqrt{8}}$$  

• $$\frac{8}{3}$$  

• $$2$$  

• $$512$$  

• $$5$$  

​Number Line Activity

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$\sqrt{95}$$  

• 8 and 9

• 9 and 10

• 10 and 11

• 11 and 12

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$\sqrt{320}$$  

• 14 and 15

• 15 and 16

• 16 and 17

• 17 and 18

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$-\sqrt{17}$$  

• -4 and -5

• -5 and -6

• -6 and -7

• -7 and -8

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$-\sqrt{156}$$  

• -9 and -10

• -10 and -11

• -11 and -12

• -12 and -13

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$\sqrt{48}$$  

• 4 and 5

• 5 and 6

• 6 and 7

• 7 and 8

Multiple Choice

What two integers is  $$\sqrt{89}$$  between?

• 85 & 90

• 7 & 8

• 8 & 9

• 9 & 10

Multiple Choice

What two integers is  $$\sqrt{250}$$  between?

• 15 & 16

• 16 & 17

• 18 & 19

• 14 & 15

Multiple Choice

What two integers is  $$\sqrt{150}$$  between?

• 10 & 11

• 11 & 12

• 12 & 13

• 13 & 14

Fill in the Blanks

Multiple Choice

Estimate the value of √18 to the nearest whole number.

• 5

• 4

• 9

• 8

Multiple Choice

Estimate the value of √118 to the nearest whole number.

• 10

• 11

• 50

• 58

Multiple Choice

$$\sqrt{11}$$ estimate and round to the nearest tenth 

• 9.2

• 5

• 11.4

• 3.2

Multiple Choice

√48 estimate and round to the nearest tenth

• 7.1

• 6.9

• 24

• 6.3

Multiple Choice

Estimate the square root to the nearest tenth: $$\sqrt{61}$$  

• 7.4

• 7.5

• 7.7

• 7.8