Rational/Irrational Numbers

Rational/Irrational Numbers

Pre- Algebra Unit 1

Multiple Choice

Convert to a fraction

 $0.\overline{12}$  

• 12/99

• 12/100

• 3/25

• 4/33

Open Ended

Convert to a fraction

 $0.\overline{51}$  

Multiple Choice

Convert 0.315 to a fraction

• 315/100

• 315/1000

• 63/200

• 315/999

What makes a Rational Number?

A number that can be written as a ration a/b is a rational number (aka Fraction)

• negative/positive whole numbers and fractions

• Terminating and Repeating Decimals

• Square Roots of Perfect square numbers

Open Ended

How do you know if a number is a rational number?

What makes an Irrational Number?

A number that cannot be written as a simple fraction

• Infinite Non Repeating Numbers - Don't end

• Square Roots of non Perfect square numbers

• pi 

Open Ended

How do you know when a number is an irrational number?

Multiple Choice

 $\sqrt{5}$  

• Rational

• Irrational

Multiple Choice

 $\overline{0.56}$  

• Rational

• Irrational

Multiple Choice

 $-\frac{3}{4}$  

• Rational

• Irrational

Multiple Choice

 $\frac{\pi}{6}$  

• Rational

• Irrational

In order to know if something is a Rational Number you must try to convert it to a fraction.

Remember a Rational Number is a number that can be written as a fraction

Place Value is super important to learn

especially when converting a number to a fraction.

Converting a Terminating Decimal into a Fraction

Steps to convert a Terminating Decimal into a Fraction

• Identify the place value of the last number

• Create fraction-decimal is the numerator is denominator, place value is denominator

• Simplify Fraction

Multiple Choice

When converting a terminating decimal to a fraction what goes in the numerator

• place value

• decimal

Multiple Choice

When writing a terminating decimal to a fraction what goes in the denominator?

• Decimal

• Place Value

Converting a repeating decimal into a fraction steps

• Subtract the non repeating number from the entire number to the right of the decimal = this is your numerator

• Determine how many numbers repeat = that is how many 9's that will be in the denominator

• count how many numbers do not repeat = that is how many 0's that will be in the denominator

• Reduce

Multiple Choice

What number is used in the denominator with repeating numbers

• 9

• 0

Multiple Choice

What number is used in the denominator for non repeating numbers?

• 9

• 0

Examples

Notice there are no zeros in these examples, why?

Multiple Choice

 $0.\overline{1}$  

• 1/2

• 1/100

• 1/10

• 1/9

Multiple Choice

 $2.\overline{4}$  

• 24/99

• 2 2/5

• 2 4/9

• 6/25

Multiple Choice

 $0.\overline{14}$  

• 7/50

• 7/45

• 14/9

• 14/99

Multiple Choice

 $0.\overline{308}$  

• 77/25

• 308/9

• 77/250

• 308/999

Multiple Choice

 $0.1\overline{8}$  

• 1  8/9

• 17/100

• 17/90

• 1  18/99

Open Ended

 $0.23\overline{7}$  

Open Ended

Convert the 0.98 into a fraction

Multiple Choice

Convert 0.36 to a fraction in simplest form

• 9/25

• 36/10

• 36/100

• 9/250

Multiple Choice

Convert 3.75 into a fraction in simplest form

• 3 & 75/100

• 3 & 2/25

• 3 & 3/4

• 3 & 1/4

Compare and Order all Number Forms

All numbers can be placed on a number line. It doesn't matter what form: fractions, decimals, percents, etc. they all go on the number line. For the harder numbers like pi or non terminating numbers we use an approximation to place it on the number line.

Number line Basics

0 is a neutral number - neither pos/neg

When you move to the right you are increasing or have more value

when you move to the left you are decreasing or have less value

Comparing Numbers in Different Forms

To compare numbers in different forms you need to convert the forms to whole numbers or decimals so you can compare them to a number line

Example

Example 2

Multiple Choice

Order From Least to Greatest

 $-25,\ \frac{72}{9},\ \sqrt{14},\ 6.5$  

•  $-25,\ \frac{72}{9},\ \sqrt{14},\ 6.5$  

•  $6.5,-25,\ \sqrt{14},\ \frac{72}{9}$  

•  $-25,\ \sqrt{14},\ \frac{72}{9},\ 6.5$  

•  $25,\ \sqrt{14},\ 6.5,\frac{72}{9}$  

Multiple Choice

Order from Greatest to Least

 $\sqrt{53},\ -\frac{12}{6},\ \ \pi\ ,\ 8$  

•  $\sqrt{53},\ -\frac{12}{6},\ \ \pi\ ,\ 8$  

•  $-\frac{12}{6},\ \ \pi\ ,\ \sqrt{53},\ 8$  

•  $\sqrt{53},\ 8\ ,\ -\frac{12}{6},\ \ \pi\$  

•  $8,\ \sqrt{53},\ \pi,\ -\frac{12}{6}$  

Poll

Stoplight Review: How do you feel about today's topic?

• Green Light - Full Speed Ahead

• Yellow Light - I'll get there slowly with practice

• Red Light - I don't know where you are at?