Converting Repeating Decimals to Fractions

The video tutorial explains how to convert repeating decimals into fractions, proving they are rational numbers. It begins with a review of rational numbers and provides examples of repeating decimals, such as 1/3. The tutorial introduces a pattern for converting repeating decimals to fractions, using examples like 0.8 repeating, 0.12 repeating, and 0.328 repeating. The process involves placing the repeating digits over a series of 9s, depending on the number of repeating digits. The video concludes by demonstrating that these conversions prove the rationality of repeating decimals.

What is a rational number?

• A number that is always a decimal

• A number that is always an integer

• A number that can be expressed as a fraction with integers

• A number that cannot be expressed as a fraction

Why are repeating decimals considered rational?

• Because they can be expressed as fractions

• Because they are irrational

• Because they are infinite

• Because they are integers

What is the repitend in a repeating decimal?

• The whole number part

• The non-repeating part

• The decimal point

• The repeating sequence of digits

How do you convert a repeating decimal with one repeating digit into a fraction?

• Place the digit over 10

• Place the digit over 9

• Place the digit over 100

• Place the digit over 1

What fraction is equivalent to 0.8 repeating?

• 8/10

• 8/9

• 8/8

• 8/11

How do you convert a repeating decimal with two repeating digits into a fraction?

• Place the digits over 99

• Place the digits over 9

• Place the digits over 100

• Place the digits over 10

What is the simplified fraction for 0.12 repeating?

• 12/99

• 4/33

• 12/9

• 1/2

How many 9s are in the denominator when converting 0.328 repeating to a fraction?

• One 9

• Two 9s

• Three 9s

• Four 9s

What fraction is equivalent to 0.328 repeating?

• 328/99

• 328/9

• 328/1000

• 328/999

Why is it important to verify the fraction obtained from a repeating decimal?

• To see if it is a whole number

• To check if it is irrational

• To confirm it is a rational number

• To ensure it is an integer