Converting Repeating Decimals into Fractions (Example)

The video tutorial explains how to convert the repeating decimal 0.42 into a fraction. It begins by defining x as 0.42 repeating and then multiplies both sides of the equation by 100 to shift the decimal. By subtracting the original equation from the new one, the repeating decimal is eliminated, allowing for the solution of x. The result is x equals 42 over 99, which simplifies to 14 over 33.

What is the repeating decimal discussed in the video?

• 0.24

• 0.42

• 0.42 repeating

• 0.24 repeating

Why do we multiply the equation by 100 in the conversion process?

• To eliminate the decimal point

• To simplify the fraction

• To make the number larger

• To move the repeating digits to the left of the decimal

What operation is performed after multiplying the equation by 100?

• Subtraction

• Division

• Multiplication

• Addition

What is the fraction obtained before simplification?

• 99 over 42

• 14 over 33

• 42 over 99

• 42 over 100

What is the simplified form of the fraction equivalent to 0.42 repeating?

• 7 over 11

• 14 over 33

• 21 over 33

• 42 over 99