Converting Repeating Decimals to Fractions

This video tutorial demonstrates how to convert repeating decimals into fractions using two examples. The first example covers converting 2.3 with a repeating 3 into a fraction, while the second example focuses on 0.02 with a repeating 2. The process involves setting up equations, multiplying to shift decimal places, subtracting equations, and simplifying the results to find the fractional equivalent of the repeating decimals.

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

• Subtract the repeating part

• Multiply the decimal by 10

• Set the repeating decimal equal to x

• Add the repeating part to itself

In the example of 2.3 repeating, what is the purpose of multiplying by 10?

• To add more repeating digits

• To simplify the fraction

• To move the repeating digit to the left of the decimal

• To eliminate the decimal

After forming the equations for 2.3 repeating, what is the next step?

• Divide by the repeating digit

• Add the equations

• Multiply by another 10

• Subtract the equations

What is the fraction equivalent of 2.3 repeating?

• 7/3

• 2/3

• 3/7

• 1/3

In the second example, what is the repeating part of 0.02?

• 0

• 2

• 02

• 20

Why do we multiply by 10 in the second example with 0.02 repeating?

• To remove the zero

• To move the repeating digit to the right

• To simplify the equation

• To add more zeros

What is the next step after forming the initial equations for 0.02 repeating?

• Add the equations

• Multiply by 100

• Subtract the equations

• Divide by 10

What is the fraction equivalent of 0.02 repeating?

• 1/90

• 2/90

• 2/45

• 1/45

What common factor is used to simplify the fraction for 0.02 repeating?

• 3

• 2

• 10

• 5

What is the final step in solving for the fraction equivalent of a repeating decimal?

• Subtract the repeating part

• Simplify the fraction

• Add the repeating part

• Multiply by 10