Question

convert (0.overline{43}) to fraction form. move numbers to the blanks to complete the fraction.

11 13 15 30 43 99 100

Explanation:

Step1: Let \( x = 0.\overline{43} \)

Let \( x \) represent the repeating decimal \( 0.434343\ldots \)

Step2: Multiply by 100

Since there are 2 repeating digits, multiply \( x \) by 100: \( 100x = 43.434343\ldots \)

Step3: Subtract the original equation

Subtract \( x = 0.434343\ldots \) from \( 100x = 43.434343\ldots \):
\( 100x - x = 43.4343\ldots - 0.4343\ldots \)
\( 99x = 43 \)

Step4: Solve for \( x \)

Divide both sides by 99: \( x = \frac{43}{99} \)

Answer:

\(\frac{43}{99}\)