Converting Repeating Decimals to Fractions

This video tutorial explains how to convert repeating decimals into fractions. It begins with setting up an equation where the variable equals the repeating decimal. The equation is then multiplied by a power of 10 to shift the decimal point, followed by subtracting the original equation to eliminate repeating parts. The resulting equation is solved to find the fraction, which is then simplified to its lowest terms. The tutorial provides a step-by-step guide to ensure understanding and preparation for a test.

What is the main topic of the video?

• Converting fractions to repeating decimals

• Graphing linear equations

• Converting repeating decimals to fractions

• Solving quadratic equations

Which digits in the decimal 0.318 are repeating?

• 3 and 1

• Only 3

• 1 and 8

• 3 and 8

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

• Multiply by a power of 10

• Simplify the fraction

• Subtract the repeating part

• Set up an equation with a variable equal to the decimal

By what power of 10 do we multiply the equation for the decimal 0.318 repeating?

• 1

• 10

• 100

• 1000

What is the result of multiplying 0.318 repeating by 100?

• 31.8

• 3.18

• 318

• 0.318

What is the purpose of subtracting the two equations?

• To eliminate the repeating part

• To find the decimal value

• To simplify the fraction

• To multiply by a power of 10

What is the resulting equation after subtracting the two equations?

• 99n = 31.5

• 10n = 3.18

• n = 0.318

• 100n = 31.8

What do we do to both sides of the equation 99n = 31.5 to solve for n?

• Multiply by 99

• Divide by 99

• Subtract 99

• Add 99

Why do we multiply the numerator and denominator by 10?

• To make the fraction larger

• To eliminate the decimal in the numerator

• To convert to a whole number

• To simplify the fraction

What is the final simplified fraction for the decimal 0.318 repeating?

• 7/22

• 315/990

• 35/110

• 31.5/99