Converting Repeating Decimals to Fractions: A Step-by-Step Guide

This video tutorial explains how to convert repeating decimals with three repeating digits into fractions. The process involves four main steps: setting up an equation, multiplying by a power of 10, subtracting equations, and solving for x. The tutorial provides two examples, highlighting the importance of aligning digits correctly to ensure accurate subtraction. The video concludes with tips for maintaining accuracy and encourages viewers to practice the method.

What is the main focus of the video tutorial?

• Converting fractions to repeating decimals

• Graphing linear equations

• Converting repeating decimals to fractions

• Solving quadratic equations

In the first step, what do we set x equal to?

• The entire repeating decimal

• The whole number part of the decimal

• The repeating part of the decimal

• The fraction form of the decimal

What power of 10 do we use to multiply the equation if three digits are repeating?

• 1000

• 10000

• 100

• 10

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

• To eliminate the decimal point

• To align the repeating digits

• To convert the decimal to a whole number

• To simplify the fraction

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

• Multiply the two equations again

• Subtract the two equations

• Divide the two equations

• Add the two equations

Why do the repeating digits cancel out when we subtract the two equations?

• Because they are different in both equations

• Because they are multiplied by zero

• Because they are added together

• Because they are the same in both equations

What is the next step after subtracting the two equations?

• Multiply by another power of 10

• Add the two equations

• Solve for x

• Convert to a decimal

How do we handle the decimal in the fraction when simplifying?

• Move the decimal point to the left

• Ignore it

• Move the decimal point to the right

• Multiply the numerator and denominator by 10 or 100

In the second example, what repeating digits are used?

• 598

• 315

• 123

• 742

What is the final step in the process?

• Check the answer with a calculator

• Convert the fraction to a decimal

• Add the two equations again

• Multiply by another power of 10