Converting Repeating Decimals to Fractions

This video tutorial from Howard Community College explains how to convert repeating decimals into fractions. It provides step-by-step examples, starting with simple cases like 0.444 repeating and moving to more complex patterns like 0.135135 and 0.2454545. The video introduces a general rule for determining the power of ten to multiply by, based on the length of the repeating pattern, and demonstrates how to simplify the resulting fractions. The tutorial concludes with a summary of the process.

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

• Multiply the decimal by 10

• Set the repeating decimal equal to n

• Divide the repeating decimal by 10

• Subtract the repeating decimal from itself

In the first example, what is the value of n when 0.444... is converted to a fraction?

• 1/9

• 1/4

• 4/9

• 4/10

For a repeating decimal with a 3-digit repeating pattern, by what power of 10 should you multiply?

• 100

• 10000

• 10

• 1000

What is the simplified fraction for the repeating decimal 0.135135...?

• 135/999

• 5/37

• 27/110

• 135/1000

What is the general rule for converting repeating decimals to fractions?

• Add the repeating decimal to itself and simplify

• Multiply by 10 and subtract

• Multiply by 10 to the power of the length of the repeating pattern, subtract, and simplify

• Divide by the length of the repeating pattern

In the third example, what is the repeating pattern of the decimal 0.2454545...?

• 45

• 24

• 54

• 245

After multiplying by 100 in the third example, what is the resulting equation?

• 100n = 24.5454...

• 100n = 245.4545...

• 100n = 0.2454...

• 100n = 2.4545...

How do you handle a fraction with a decimal in the numerator?

• Leave it as is

• Multiply both the numerator and the denominator by 10

• Divide the numerator by 10

• Subtract the decimal part from the numerator

What is the simplified fraction for the repeating decimal 0.2454545...?

• 27/110

• 243/990

• 24/99

• 5/37

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

• Simplify the fraction

• Multiply by 10

• Subtract the equations

• Set the decimal equal to n