Converting Repeating Decimals to Fractions

The video tutorial explains how to convert repeating decimals into fractions using two examples. The first example demonstrates the conversion of 0.86 with the six repeating, while the second example covers 3.152 with the five and two repeating. Each example follows a step-by-step process involving setting the decimal equal to a variable, multiplying to shift the decimal, forming equations, and solving for the variable to find the fraction equivalent. The tutorial emphasizes checking the results using a calculator.

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

• Set the repeating decimal equal to x

• Divide by the number of repeating digits

• Multiply the decimal by 10

• Subtract the repeating part

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In the first example, what is the purpose of multiplying the equation by 10?

• To eliminate the repeating part

• To move the decimal point

• To simplify the fraction

• To add a whole number

What is the result of simplifying the fraction 78/90?

• 39/45

• 19/22

• 13/15

• 26/30

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In the second example, which digits are repeating in the decimal 3.152?

• 2 and 3

• 3 and 1

• 5 and 2

• 1 and 5

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What is the first step in converting the decimal 3.152 with repeating 5 and 2?

• Add a whole number

• Subtract the repeating part

• Set x equal to the repeating decimal

• Multiply by 100

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

• To move the decimal two places to the right

• To eliminate the repeating part

• To add a whole number

• To simplify the fraction

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What is the fraction form of the repeating decimal 0.152 with repeating 5 and 2?

• 153/990

• 151/990

• 150/990

• 152/1000

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How do you verify the fraction obtained from a repeating decimal?

• By multiplying the fraction by 10

• By dividing the numerator by the denominator

• By adding the fraction to a whole number

• By subtracting the fraction from 1

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What is the mixed number form of 3.152 with repeating 5 and 2?

• 3 and 150/990

• 3 and 152/1000

• 3 and 151/990

• 3 and 153/990

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

• Multiply by 10

• Subtract the equations

• Divide by the number of repeating digits

• Add a whole number

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