Converting Repeating Decimals to Fractions

This video tutorial from Mumo Math explains a shortcut for converting repeating decimals into fractions. It covers the rules for determining numerators and denominators, provides examples, and highlights exceptions. The tutorial includes both simple and complex examples to illustrate the process, ensuring viewers understand how to handle different types of repeating decimals.

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

• Add the repeating digits together.

• Divide the decimal by 2.

• Multiply the decimal by 10.

• Identify the repeating and non-repeating parts.

How do you write the denominator for a repeating decimal like 0.333...?

• Use 9 as the denominator.

• Use 10 as the denominator.

• Use 3 as the denominator.

• Use 1 as the denominator.

What is the fraction form of the repeating decimal 0.666...?

• 3/4

• 2/3

• 5/6

• 1/2

When dealing with a mixed recurring decimal like 0.166..., what should you do with the non-repeating part?

• Add it to the repeating part.

• Ignore it.

• Subtract it from the repeating part.

• Multiply it by 10.

For a decimal like 0.833..., what is the correct numerator after subtraction?

• 83

• 90

• 75

• 8

In a special case where the decimal is 0.4166..., how many non-repeating digits should be considered?

• Four

• Two

• One

• Three

What is the reduced fraction form of 0.4166...?

• 11/12

• 7/12

• 13/12

• 5/12

How do you handle a repeating decimal with a complex pattern like 0.251818...?

• Divide by 10.

• Add all digits together.

• Subtract the non-repeating part from the repeating part.

• Multiply by 100.

What is the first step in verifying a complex repeating decimal conversion?

• Add zeros to the denominator.

• Multiply the fraction by 10.

• Check the subtraction result.

• Use a calculator to divide the numbers.

For a number like 0.706438889..., how many zeros should be added to the denominator?

• Five

• Four

• Three

• Two