Question

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10
write the repeating decimal below as a fraction.
0.\overline{14}

Explanation:

Step1: Identify the repeating decimal

The repeating decimal is \(0.\overline{14}\), where the bar is over "14", meaning "14" repeats indefinitely. Let \(x = 0.\overline{14}\).

Step2: Multiply by a power of 10 to shift the decimal

Since there are 2 repeating digits, multiply \(x\) by \(100\) (because \(10^2 = 100\)):
\(100x = 14.\overline{14}\)

Step3: Subtract the original equation from the new one

Subtract \(x = 0.\overline{14}\) from \(100x = 14.\overline{14}\):
\(100x - x = 14.\overline{14} - 0.\overline{14}\)
\(99x = 14\)

Step4: Solve for \(x\)

Divide both sides by \(99\):
\(x = \frac{14}{99}\)

Answer:

\(\frac{14}{99}\)