Expressing Rational Numbers as Repeating Decimals (Part 2 )

The video tutorial explains how whole numbers and rational numbers can be expressed as repeating decimals. It begins by demonstrating that whole numbers can be written as fractions and then converted to decimals with repeating zeros. The tutorial then explores how rational numbers, such as 2/3, 4/9, and 3/11, can have repeating decimal forms with varying numbers of repeating digits. The key takeaway is that any rational number will eventually have a repeating decimal expansion.

How can a whole number be expressed as a repeating decimal?

• By dividing it by 2

• By multiplying it by 10

• By converting it into a fraction over 1

• By adding zeros at the end

What is the repeating decimal form of 2/3?

• 0.3 repeating

• 0.6 repeating

• 0.9 repeating

• 0.2 repeating

Which of the following fractions has two repeating digits in its decimal form?

• 1/3

• 4/7

• 2/5

• 3/11

What is the decimal representation of 4/9?

• 0.5 repeating

• 0.4 repeating

• 0.7 repeating

• 0.6 repeating

What is a key characteristic of the decimal expansion of any rational number?

• It will eventually terminate

• It will eventually repeat

• It will always be a whole number

• It will always be irrational