Repeating Decimals to Fractions and Vice Versa

Repeating Decimals

Unit 1

Decimals can be written as Fractions and Fractions can be written as Decimals

Even repeating numbers can be written as fractions, and decimals

Steps to Write Fractions as Repeating Decimals

• divide the numerator(top #) by the denominator (bottom #)

What is a repeating Decimal?

Multiple Choice

Select the decimal that is equivalent to 19/27

• 0.626

• 0.703

• $0.\overline{703}$
  

• $0.\overline{626}$

• None of the Above

Multiple Choice

Select the decimal that is equivalent to $\frac{13}{75}$  

• 0.21

•  $0.\overline{21}$  

• 0.3

•  $0.\overline{3}$  

• None of the Above

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?

Open Ended

 $0.\overline{2}$  

Rewrite as a simplified fraction

Open Ended

 $3.\overline{1}$  

Rewrite as a simplified fraction.

Open Ended

 $0.8\overline{3}$  

Rewrite as a simplified fraction.

Open Ended

 $3.8\overline{3}$  

Rewrite as a simplified fraction.

Open Ended

 $0.48\overline{2}$  

Rewrite as a simplified fraction.

Open Ended

 $2.31\overline{4}$  

Rewrite as a simplified fraction.

Poll

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

• Green Light - Full Speed Ahead

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

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