What is 18.103846384638463846... as a Fraction?

18.103846 equals 150850383325 as a fraction.

How do you turn 18.103846 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.103846 repeating into a fraction, begin writing this simple equation:

n = 18.103846 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3846) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 18103846.3846 (equation 2)

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

1000000 × n = 18103846.3846
    100 × n = 18.103846
 999900 × n = 18102036

18102036999900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 12 (the GCF - greatest common factor).

n = 18102036999900 = 18102036 ÷ 12999900 ÷ 12 = 150850383325. So,

18.103846 = 150850383325 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 150850383325 is also equal to 18865383325 when expressed as a mixed number.

The repeating decimal 18.103846 (vinculum notation) has a repeated block length of 4. It is also represented as 18.10384638463846... (ellipsis notation) which equals approximately 18.1038463846384638463846 (decimal approximation)(*).

The recurring decimal 18.103846 can be written as a ratio of two integers having 1508503 as the numerator and 83325 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.