Converting Repeating Decimals to Fractions

This video tutorial explains how to convert repeating decimals into fractions, demonstrating that repeating decimals are rational numbers. It provides step-by-step instructions for converting both single and two-digit repeating decimals using algebraic methods. The video includes examples to illustrate the process and concludes with a prompt to subscribe for more math and science content.

What distinguishes a repeating decimal from an irrational number like pi?

• Repeating decimals cannot be expressed as fractions.

• Repeating decimals are always greater than one.

• Repeating decimals have a sequence of digits that repeat indefinitely.

• Repeating decimals have a finite sequence of digits.

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

• Subtract the decimal from one.

• Add the decimal to itself.

• Set the decimal equal to a variable.

• Multiply the decimal by 100.

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In the example of converting 0.444... to a fraction, what is the resulting fraction?

• 2/5

• 4/9

• 1/3

• 5/11

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When dealing with a two-digit repeating decimal, what should you multiply the variable by?

• 1000

• 10

• 100

• 1

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What is the simplified fraction for the repeating decimal 0.0909...?

• 9/99

• 1/9

• 3/33

• 1/11

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How do you handle a repeating decimal greater than one, like 1.333...?

• Subtract the integer part and convert the decimal part.

• Ignore the integer part and convert the decimal part.

• Add the integer part to the decimal part.

• Multiply the entire number by 10.

What is the fraction form of 1.333...?

• 3/2

• 7/5

• 5/4

• 4/3

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For a two-digit repeating decimal greater than one, like 123.2323..., what is the first step?

• Add 1

• Subtract 1

• Multiply by 100

• Multiply by 10

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What is the fraction form of 123.2323...?

• 124/101

• 123/100

• 125/102

• 122/99

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What is the key takeaway from converting repeating decimals to fractions?

• Repeating decimals can always be expressed as fractions.

• Repeating decimals are always less than one.

• Repeating decimals cannot be simplified.

• Repeating decimals are irrational numbers.

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