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express 32.1235 repeating bar on 1235 in p/q form.
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express 32.1235 repeating bar on 1235 in p/q form.
Expressing 32.1235 Repeating Bar on 1235 in p/q Form


Understanding the Problem

Before we start, we need to understand what the repeating bar means. A repeating bar, also called a repeating decimal, is a decimal that has a pattern that repeats indefinitely. In the case of 32.1235 repeating bar on 1235, the pattern is 1235, which repeats forever.


Converting to p/q Form

To express a repeating decimal in p/q form, we need to follow these steps:



  • Let x be the repeating decimal.

  • Count the number of digits in the repeating pattern and call it n.

  • Multiply x by 10^n to get rid of the repeating pattern.

  • Subtract x from the result of step 3 to eliminate the non-repeating part.

  • Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor.



Applying the Formula

Let's apply the formula to 32.1235 repeating bar on 1235:



  • x = 32.1235 repeating bar on 1235

  • n = 4 (since the repeating pattern has 4 digits)

  • 10^n = 10^4 = 10000

  • 10^n x = 321235.1235 repeating bar on 1235

  • 10^n x - x = 321235.1235 repeating bar on 1235 - 32.1235 repeating bar on 1235 = 321203

  • x (10^n - 1) = 32.1235 repeating bar on 1235 (10000 - 1) = 321235.1235 repeating bar on 1235 - 32.1235 repeating bar on 1235 = 321203

  • x = (321203)/(9999)

  • x = (357)/111



Final Answer

Therefore, 32.1235 repeating bar on 1235 in p/q form is (357)/111.
Community Answer
express 32.1235 repeating bar on 1235 in p/q form.
321203/9999
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express 32.1235 repeating bar on 1235 in p/q form.
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