Converting Repeating Decimals to Fractions

The video tutorial explains how to convert repeating decimals into fractions in their simplest form. It begins by comparing repeating decimals with terminating decimals and demonstrates the conversion process using algebraic methods. The tutorial shows how to multiply the repeating decimal by a power of 10 to align the repeating parts, subtract to eliminate the repeating section, and solve for the fraction. Finally, it simplifies the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. The video concludes with a brief mention of exploring more examples in future lessons.

What is the first step in converting a terminating decimal like 0.5 to a fraction?

• Find the GCD

• Put the number over 10

• Multiply by 10

• Subtract the decimal part

What does the bar over the digits in a repeating decimal indicate?

• The digits are whole numbers

• The digits are irrational

• The digits terminate

• The digits repeat indefinitely

Why do we multiply both sides of the equation by 100 in the example with 0.272727...?

• To simplify the fraction

• To make the number larger

• To shift the decimal point two places to the right

• To eliminate the decimal point

What is the result of subtracting X from 100X in the example?

• 100X

• 99X

• 0

• X

What happens to the repeating part of the decimal when you subtract the two equations?

• It cancels out

• It remains the same

• It doubles

• It becomes zero

What is the simplified form of the fraction 27/99?

• 27/9

• 1/3

• 9/33

• 3/11

What is the GCD of 27 and 99?

• 3

• 9

• 27

• 11

What is the purpose of finding the GCD when simplifying a fraction?

• To add the numerator and denominator

• To multiply the numerator and denominator

• To convert the fraction to a decimal

• To find the largest common factor

If a repeating decimal has three repeating digits, by what power of 10 should you multiply?

• 1000

• 100

• 10

• 10000

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

• Finding the GCD

• Multiplying by 10

• Subtracting the equations

• Adding the numerator and denominator