Converting Repeating Decimals to Fractions

The video tutorial explains how to convert repeating decimals into fractions using two examples. The first example demonstrates the conversion of 0.86 with the repeating digit 6 into a fraction. The process involves setting the decimal equal to x, multiplying by powers of 10 to align repeating digits, and solving the resulting equations. The second example covers the conversion of 3.15 with repeating digits 5 and 2, following a similar method. The tutorial emphasizes checking results with a calculator and provides a detailed step-by-step approach to ensure understanding.

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

• Set the repeating decimal equal to x

• Multiply the decimal by 10

• Divide by the repeating number

• Subtract the repeating part

In the example of 0.86 with the 6 repeating, what is the purpose of multiplying by 10 in step two?

• To simplify the fraction

• To move the decimal point

• To eliminate the repeating part

• To add a whole number

What is the simplified fraction form of 0.86 with the 6 repeating?

• 39/45

• 78/90

• 26/30

• 13/15

When converting 3.15 with the 5 and 2 repeating, what is left out initially?

• The repeating part

• The whole number 3

• The decimal point

• The number 5

What is the equation formed in step two for 3.15 with the 5 and 2 repeating?

• x = 3.152

• 10x = 1.52

• 100x = 15.2

• x = 0.152

How many places do you move the decimal to the right to have 5 and 2 to the left of the decimal in 3.15?

• One place

• Two places

• Four places

• Three places

What is the final fraction form of 3.15 with the 5 and 2 repeating?

• 78/90

• 39/45

• 3121/990

• 151/990

What is the mixed number form of 3.15 with the 5 and 2 repeating?

• 3 and 3121/990

• 3 and 151/990

• 3 and 39/45

• 3 and 78/90

What is the purpose of subtracting equation two from equation three in the conversion process?

• To find the common factor

• To simplify the equation

• To isolate the repeating part

• To eliminate the whole number

How can you verify the fraction obtained from a repeating decimal?

• By checking with a calculator

• By multiplying by 10

• By adding a whole number

• By dividing by the repeating number