Converting Repeating Decimals to Fractions

This video tutorial explains how to convert repeating decimals into fractions. It begins with an introduction to the concept and outlines the steps involved: setting up equations, aligning repeating decimals, and solving for X. The tutorial includes four examples, ranging from simple to complex, demonstrating the process of converting repeating decimals, including those with non-repeating parts, into fractions. The video concludes with a summary of the steps and encourages viewers to subscribe for more math and science content.

What is the first step in converting a repeating decimal to a fraction?

• Multiply the decimal by 10

• Set up an equation with X equal to the repeating decimal

• Subtract the repeating part from the decimal

• Divide the decimal by 9

In the example of converting 0.333... to a fraction, what is the value of 10X?

• 1.333...

• 33.333...

• 0.333...

• 3.333...

What is the fraction form of 0.333...?

• 1/4

• 1/3

• 1/5

• 1/2

In the example of converting 0.1818... to a fraction, what is the value of 100X?

• 181.818...

• 1.818...

• 18.1818...

• 0.1818...

What is the simplified fraction form of 0.1818...?

• 5/11

• 3/11

• 2/11

• 4/11

In the example of converting 0.1666... to a fraction, what is the repeating part?

• 1

• 6

• 66

• 666

What is the fraction form of 0.1666...?

• 1/3

• 1/6

• 1/4

• 1/5

In the example of converting 5.1818... to a fraction, what is the value of 100X?

• 5.1818...

• 51.818...

• 518.1818...

• 5181.818...

What is the simplified fraction form of 5.1818...?

• 60/11

• 59/11

• 58/11

• 57/11

What is the general method to convert any repeating decimal to a fraction?

• Multiply by 100 and subtract

• Set X to the decimal, create a second equation, subtract, and simplify

• Divide by 9 and simplify

• Add the repeating part to the decimal