Convert Repeating Decimals to Fractions

Converting Repeating Decimals to Fractions

By the end of the lesson, ​you will be able to apply the algorithm for converting repeating decimals to fractions using mathematical reasoning and problem solving.

​Repeating Decimals to Fractions

• ​Watch the video

• ​Record the examples on your guided notes page as you watch

• ​Ask questions if you don't understand!!

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

Convert 0.444... to a fraction.

• 4/10
• 4.4/99
• 4/9
• 2/5

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

• 2/3
• -2/3
• 3/5
• -3/5

Multiple Choice

0.33333 is considered a ________ decimal

• repeating
• terminating

Multiple Choice

A fraction is which type of number?

• Rational
• Irrational
• Integer
• Whole

Multiple Choice

Rational numbers can always be written as a __________.

• fraction

• decimal

• negative number

• whole number

Multiple Choice

A ______ decimal has a finite number of digits, meaning that after a so many places, the decimal ends.

• non-terminating

• terminating

• repeating

Multiple Choice

A _______ decimal continues infinitely without ending in a sequence of zeros.

• non-terminating

• repeating

• terminating

Multiple Choice

A ______ decimal is a decimal in which a digit, or a group of digits, repeat(s) infinitely

• non-terminating

• terminating

• repeating

Multiple Choice

Convert the following decimal into a fraction. 

$$0.\overline{36}$$  

• 4/9

• 4/11

• 4/13

• 3/13

Fill in the Blank

Write as a decimal:

$$\frac{4}{5}$$  

.

Fill in the Blank

What number is used as the denominator when repeating decimals are converted to fractions? (Hint: See a line, write a ... )

Fill in the Blank

Write the decimal as an equivalent fraction.

/

Fill in the Blank

Convert 0.252525... to a fraction.

/

Multiple Select

Select all equivalent fractions.

• 3/10

• 1/3

• 3/9

• 30/99

Fill in the Blank

Convert the following decimal to a fraction in simplest form. 0.6

Fill in the Blank

Convert the following decimal to a fraction in simplest form. 0.79

/

Poll

How well did you understand this lesson?