Converting Repeating Decimals into Fractions: Proving Rationality

The video tutorial explains how to convert repeating decimals into fractions, proving they are rational numbers. It begins by defining rational numbers and questioning the rationality of repeating decimals. The tutorial then introduces a method for converting repeating decimals into fractions by placing the repetend over a series of 9s. Examples such as 0.8 repeating, 0.12 repeating, and 0.328 repeating are used to demonstrate the conversion process, confirming their rationality.

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

What is the repetend in a repeating decimal?

• The digits that repeat in the decimal

• The whole number part of the decimal

• The non-repeating part of the decimal

• The number of zeros in the decimal

How do you convert 0.8 repeating into a fraction?

• Put 8 over 10

• Put 8 over 9

• Put 8 over 100

• Put 8 over 99

What fraction is equivalent to 0.12 repeating?

• 12/99

• 1/9

• 12/90

• 4/33

How many nines do you use in the denominator for 0.328 repeating?

• One 9

• Two 9s

• Four 9s

• Three 9s

What is the fraction form of 0.328 repeating?

• 32/9

• 328/1000

• 32/99

• 328/999

Why are repeating decimals considered rational?

• They are always whole numbers

• They can be expressed as a fraction

• They never end

• They are irrational numbers