Simplifying Repeating Decimals

This video tutorial explains how to convert repeating decimals into fractions using two examples: 0.7 repeating and 0.81 repeating. The process involves setting up equations, multiplying to shift decimal places, and subtracting to isolate the repeating part. The video also highlights a pattern in the conversion process, noting that it only applies when all digits repeat. The tutorial concludes with a hint at future examples where this pattern may not hold.

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

• Multiply the decimal by 10

• Set the decimal equal to x

• Subtract the decimal from 1

• Divide the decimal by 10

In the example of 0.7 repeating, what is the result of subtracting the two equations?

• x = 1/7

• x = 9/7

• x = 1/9

• x = 7/9

What is the repeating decimal used in the second example?

• 0.7

• 0.81

• 0.9

• 0.18

How many places do you move the decimal to the right for 0.81 repeating?

• Three places

• Four places

• Two places

• One place

What is the simplified fraction for 0.81 repeating?

• 10/11

• 7/9

• 9/11

• 8/9

What is the common factor used to simplify 81/99?

• 12

• 3

• 6

• 9

What is the result of multiplying 0.81 repeating by 100?

• 81.81 repeating

• 0.81 repeating

• 810.81 repeating

• 8.1 repeating

What is the purpose of multiplying the equation by multiples of 10?

• To eliminate the decimal

• To make the decimal larger

• To move repeating digits to the left of the decimal

• To make the equation simpler

What pattern is observed in the examples provided?

• The fraction is formed by the repeating digits over nines

• The fraction is always improper

• The denominator is always 9

• The numerator is always 1

When does the observed pattern not hold true?

• When all digits repeat

• When the decimal is less than 0.5

• When some digits do not repeat

• When no digits repeat