What is 104.111... as a Fraction?

104.1 equals 9379 as a fraction.

How do you turn 104.1 repeating into a fraction?

Detailed Answer:

Step 1: To convert 104.1 repeating into a fraction, begin writing this simple equation:

n = 104.1 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (1), so multiply both sides by 10¹ = 10.

10 × n = 1041.1 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

10 × n = 1041.1
 1 × n = 104.1
 9 × n = 937

n = 9379 (answer)

104.1 = 9379 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 9379 is also equal to 10419 when expressed as a mixed number.

The repeating decimal 104.1 (vinculum notation) has a repeated block length of 1. It is also represented as 104.111... (ellipsis notation) which equals approximately 104.11111 (decimal approximation)(*).

The recurring decimal 104.1 can be written as a ratio of two integers having 937 as the numerator and 9 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.