Pre-Algebra 20 - Converting Repeating Decimal Numbers to Fractions

The video tutorial explains how to convert repeating decimal numbers into fractions. It begins with a review of multiplying decimals by 10 and converting finite decimals to fractions. The tutorial then provides step-by-step examples of converting repeating decimals, such as repeating fives, threes, and sequences like 142857, into fractions. Each example demonstrates the process of eliminating repeating digits through multiplication and subtraction, simplifying equations, and reducing fractions. The tutorial concludes with a brief introduction to the next topic, exponentiation.

What is the first step in converting a repeating decimal with a single repeating digit into a fraction?

• Add the repeating digit

• Multiply the number by 10

• Subtract the repeating digit

• Multiply the number by 100

How do you simplify the equation when converting a repeating decimal with a single repeating digit?

• Subtract the fraction from 10 times itself

• Multiply both sides by 9

• Divide both sides by 10

• Add the fraction to itself

When converting a repeating decimal with a sequence of three digits, what is the equivalent multiplication factor?

• 100

• 1000

• 10

• 10000

What is the result of dividing both sides of the equation by 999 when converting a repeating decimal with three repeating digits?

• The fraction is simplified

• The repeating digits are eliminated

• The equation becomes invalid

• The fraction becomes a whole number

How can you handle a non-integer result when converting a repeating decimal to a fraction?

• Ignore the decimal part

• Multiply the numerator and denominator by 10

• Add 1 to the numerator

• Subtract 1 from the denominator

What is the final step in converting a complex repeating decimal sequence into a fraction?

• Simplify the fraction

• Subtract the original number

• Add the repeating sequence

• Multiply by 10

What is the equivalent fraction for the repeating decimal sequence 142857?

• 1/6

• 1/7

• 1/9

• 1/8