QQuestionMathematics
QuestionMathematics
Express the recurring decimal $0 . \overline{56}$ as a fraction in its simplest form.
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Answer
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Step 1:: Identify the pattern in the decimal
The given decimal number is $0.565656...$, and the pattern starts from the third decimal place and repeats indefinitely.
Step 2:: Multiply the number by a suitable power of 10
0.565656... imes 10^{2} = 56.565656...
In this case, $n= 1$. So,
Step 3:: Subtract the original number from the result
56.565656... - 0.565656... = 56
Subtract the original number from the result obtained in Step 2:
Step 4:: Observe that the difference is a whole number
Since the difference is a whole number, we can express the recurring decimal as a fraction.
Step 5:: Divide the whole number by the power of 10 used in Step 2
\frac{56}{10^{2}} = \frac{56}{100}
Divide the whole number obtained in Step 4 by the power of 10 used in Step 2:
Final Answer
The recurring decimal $0.565656...$ can be expressed as the fraction $\frac{56}{100}$ in its simplest form.
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