Converting Repeating Decimals to Fractions

The video tutorial explains how to convert repeating decimals into fractions using a four-step process. It begins with writing an equation for the repeating decimal, then multiplying the equation to shift the decimal point. Next, it involves subtracting the original equation from the new one to eliminate repeating parts, and finally solving for x and simplifying the fraction. The tutorial includes examples to illustrate the process, ensuring a clear understanding of each step.

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

• Multiply the decimal by 10

• Write the repeating decimal as an equation

• Subtract the repeating part

• Simplify the fraction

In the example 0.25 repeating, what does x equal?

• 0.25

• 0.255555...

• 0.2

• 2.5

What is the purpose of multiplying the equation by a power of 10?

• To simplify the fraction

• To make the number larger

• To shift the decimal point to the right

• To eliminate the decimal point

If one digit is repeating, by what number should you multiply the equation?

• 1000

• 10

• 1

• 100

What do you do after creating the second equation by multiplying?

• Add the two equations

• Divide the two equations

• Subtract the original equation from the new equation

• Multiply the two equations

What is the result of subtracting the original equation from the new equation in the example 0.25 repeating?

• 0.3

• 3.0

• 2.0

• 2.3

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

• Multiply by 10

• Subtract the equations

• Solve for x and simplify the fraction

• Write the repeating decimal as an equation

Why do you multiply the top and bottom of the fraction by 10 or 100?

• To make the fraction larger

• To make the fraction smaller

• To eliminate the decimal point

• To add more digits

In the second example, what is the repeating decimal?

• 0.381

• 0.38

• 0.3

• 0.381111...

What is the fraction form of 0.381 repeating?

• 34/90

• 343/1000

• 3.43/9

• 343/900