Solving Repeating Decimals Equations

The video tutorial explains how to convert a repeating decimal into a fraction. It begins by defining the repeating decimal as a variable x. Then, it multiplies both sides of the equation by 10 to shift the decimal point, making it easier to eliminate the repeating part. By subtracting the original equation from the new one, the repeating decimals cancel out, leaving a simple equation to solve for x. The tutorial concludes by showing that the repeating decimal 0.55 is equivalent to the fraction 5/9.

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

• Multiply the decimal by 10

• Add the repeating decimal to itself

• Set the repeating decimal equal to a variable

• Subtract the repeating part

What operation is performed after setting x equal to the repeating decimal?

• Division

• Addition

• Subtraction

• Multiplication

If x equals 0.55 repeating, what is the next step after setting up the equation?

• Add 1 to both sides

• Multiply both sides by 10

• Subtract 0.5 from both sides

• Divide by 10

What does multiplying both sides of the equation by 10 accomplish?

• It changes the decimal to a whole number

• It moves the decimal point one place to the right

• It makes the equation easier to solve

• It cancels out the repeating part

After multiplying by 10, what is the equation for 10x?

• 10x = 5.55 repeating

• 10x = 55

• 10x = 5.5

• 10x = 0.55

What is the value of 10x if x equals 0.55 repeating?

• 0.55

• 5.5

• 55

• 5.55 repeating

What is the purpose of moving the decimal point when multiplying by 10?

• To make the number larger

• To simplify the equation

• To eliminate the repeating part

• To align the decimals

What is the purpose of subtracting the original equation from the multiplied equation?

• To eliminate the repeating decimal

• To find the value of x

• To add the repeating parts

• To simplify the equation

What is the result of subtracting x from 10x in this context?

• 9x = 0.5

• 9x = 0

• 9x = 55

• 9x = 5

Why does the repeating part cancel out when subtracting the equations?

• Because they are multiplied

• Because they are added

• Because they are different

• Because they are equal