What is \( 0.\overline{185} \) as a fraction?

0.185 1000 x = 185.185 − x = − 0.185 − − − − − − 999 x = 185 / : 999 x = 999 185 ​ x = 27 5 ​

Answered by Lilith | 2024-06-10

The fraction 185/999 is the simplified form of the repeating decimal 0.185.
We have,
To convert the repeating decimal 0.185 (where the digit 5 repeats infinitely) into a fraction, we can use a technique called geometric series.
Let's represent the repeating decimal as x:
x = 0.185185185...
Now, multiply both sides of the equation by 1000 (since there are three digits in the repeating pattern):
1000x = 185.185185...
Next, subtract the original equation from this new equation to eliminate the repeating part:
1000x - x = 185.185185... - 0.185185...
Simplifying the equation:
999x = 185
Divide both sides of the equation by 999 to solve for x:
x = 185 / 999
Thus,
The fraction 185/999 is the simplified form of the repeating decimal 0.185.
Learn more about fractions here:
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Answered by swapnalimalwadeVT | 2024-06-17

The repeating decimal 0. 185 can be expressed as the fraction 27 5 ​ after a series of algebraic manipulations. This involves setting the decimal equal to a variable, multiplying to shift the decimal point, and simplifying the resulting fraction. The final simplified fraction is obtained by finding the greatest common divisor of the numerator and denominator.
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Answered by Lilith | 2024-09-26