Converting Repeating Decimals to Fractions

The video tutorial demonstrates how to convert a repeating decimal into a fraction. It begins by setting the repeating decimal equal to a variable, x. The process involves aligning the repeating digits to the right of the decimal by multiplying by powers of ten, then moving them to the left by further multiplication. The tutorial continues by subtracting equations to isolate x and solve for it, simplifying the resulting fraction, and verifying the solution. The example used is 4.0536 with the digits 3 and 6 repeating.

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

• Set the repeating decimal equal to x

• Multiply by 10

• Add the repeating digits

• Subtract the non-repeating part

Why do we multiply the equation by 100 in the second step?

• To move the repeating digits to the right of the decimal

• To eliminate the decimal point

• To simplify the equation

• To convert the decimal to a whole number

What is the purpose of moving the repeating digits to the left of the decimal?

• To make the number larger

• To prepare for subtraction

• To simplify the fraction

• To eliminate the repeating part

What operation is performed after setting up the equations with repeating digits on both sides?

• Subtraction

• Multiplication

• Division

• Addition

How do we simplify the fraction obtained from the subtraction step?

• By adding the numerator and denominator

• By dividing both by their greatest common factor

• By subtracting the numerator from the denominator

• By multiplying both by 10

What is the final form of the repeating decimal 4.0536 with 3 and 6 repeating?

• 4 and 59/1100

• 4.0536

• 4 and 59/900

• 4 and 59/100

What is the result of dividing 531 by 9?

• 58

• 53

• 59

• 60

What is the improper fraction form of the repeating decimal?

• 4459/1100

• 4459/1200

• 4459/900

• 4459/1000

How can you verify the conversion of a repeating decimal to a fraction?

• By adding the fraction to itself

• By multiplying the fraction by 10

• By dividing the numerator by the denominator

• By subtracting the fraction from 1

What common factor is used to simplify the fraction 531/9900?

• 9

• 5

• 3

• 11