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QuestionMathematics
What is the recurring decimal 0.1 as a fraction in its simplest form?
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Step 1:: To express the recurring decimal 0.1 as a fraction, we need to find a numerator and denominator such that when the decimal is expressed as a fraction, it terminates or repeats.
In this case, the repeating decimal 0.1 repeats indefinitely.
Step 2:: We can think of 0.1 as 1 / 10, but since it repeats indefinitely, we need to multiply both the numerator and denominator by 10 until the repeating pattern is contained within the numerator.
\begin{align*}
Step 3:1 &= \frac{1}{10} \
&= \frac{10}{100} \ \end{align*}
Step 4:: We have now expressed 0.1 as a fraction by multiplying both the numerator and denominator by 10 until the repeating pattern is contained within the numerator.
We then simplified the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5 in this case.
Final Answer
The recurring decimal 0.1 as a fraction in its simplest form is 1 / 10.
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