To solve the given problem, we need to write the number 0.84181 as a fraction in lowest terms. We will follow the steps below to find the answer.


To convert the recurring decimal 0.84181(81) to a fraction, we can use the following steps:

1. Let x = 0.84181(81).
2. Multiply both sides of the equation by 100 to remove the decimal: 100x = 84.181(81).
3. Subtract the original equation from the multiplied equation to eliminate the recurring part: 100x - x = 84.181(81) - 0.84181(81).
This simplifies to: 99x = 83.339.
4. Divide both sides of the equation by 99 to solve for x: x = 83.339 / 99.


To simplify the fraction 83.339 / 99, we need to express it in lowest terms. We can do this by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

1. The GCD of 83.339 and 99 is 1 since there are no common factors other than 1.
2. Divide both the numerator and denominator by the GCD: 83.339 / 99 = (83.339 ÷ 1) / (99 ÷ 1) = 83.339 / 99.


To find the difference between the denominator and numerator, we subtract the numerator from the denominator.

1. Numerator = 83.339
2. Denominator = 99
3. Difference = Denominator - Numerator = 99 - 83.339 = 15.661.


In the given problem, when the decimal 0.84181(81) is written as a fraction in lowest terms, the denominator exceeds the numerator by 15.661. This means that the denominator (99) is greater than the numerator (83.339) by 15.661.