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write 0.878787... as a fraction in simplest form.
select one:
a. \\(\frac{9}{10}\\)
b. \\(\frac{87}{10000}\\)
c. \\(\frac{87}{100}\\)
d. \\(\frac{29}{33}\\)

Explanation:

Step1: Identify the repeating decimal

The decimal is \(0.\overline{87}\) (0.878787...), where 87 repeats. Let \(x = 0.878787...\)

Step2: Multiply by 100 to shift the decimal

Since the repeating cycle is 2 digits, multiply \(x\) by 100: \(100x = 87.878787...\)

Step3: Subtract to eliminate the repeating part

Subtract \(x\) from \(100x\): \(100x - x = 87.8787... - 0.8787...\)
This simplifies to \(99x = 87\)

Step4: Solve for \(x\)

Divide both sides by 99: \(x=\frac{87}{99}\)

Step5: Simplify the fraction

Divide numerator and denominator by their GCD (3): \(\frac{87\div3}{99\div3}=\frac{29}{33}\)

Answer:

d. \(\frac{29}{33}\)