Converting Repeating Decimals to Fractions

This video tutorial explains how to convert repeating decimals into fractions, also known as rational numbers. It begins with an introduction to rational numbers and their representation as a ratio of integers. The video provides two examples: converting 2.3535... and 0.31212... into fractions. The process involves multiplying the decimal to shift the repeating part, subtracting to eliminate it, and solving for the fraction. The tutorial concludes with a suggestion to watch another video for more practice.

What is a rational number?

• A number that cannot be expressed as a fraction

• A number that can be expressed as a ratio of two integers

• A number with a non-repeating decimal

• A number that is always positive

In the first example, what is the repeating part of the decimal?

• 3535

• 35

• 2

• 99

Why do we multiply by 100 in the first example?

• To move the decimal two places to the right

• To eliminate the decimal

• To simplify the fraction

• To make the number larger

What is the fraction form of 2.353535...?

• 2 and 100/35

• 2 and 35/99

• 2 and 35/100

• 2 and 99/35

In the second example, what is the repeating part of the decimal?

• 1212

• 3

• 12

• 312

Why do we multiply by 1000 in the second example?

• To simplify the fraction

• To make the number larger

• To move the decimal three places to the right

• To eliminate the decimal

What is the fraction form of 0.3121212...?

• 103/330

• 312/1212

• 309/990

• 1000/312

How can you verify the fraction obtained from a repeating decimal?

• By adding the numerator and denominator

• By dividing the numerator by the denominator

• By subtracting the numerator from the denominator

• By multiplying the fraction by 10

What should you do if you want more practice on converting repeating decimals?

• Watch another video

• Read a book

• Practice on paper

• Ask a friend