What is 12.13999... as a Fraction?

12.139 equals 60750 as a fraction.

How do you turn 12.139 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.139 repeating into a fraction, begin writing this simple equation:

n = 12.139 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (9) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 12139.9 (equation 2)

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

1000 × n = 12139.9
 100 × n = 12.139
 900 × n = 10926

10926900 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 18 (the GCF - greatest common factor).

n = 10926900 = 10926 ÷ 18900 ÷ 18 = 60750. So,

12.139 = 60750 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 60750 is also equal to 12750 when expressed as a mixed number.

The repeating decimal 12.139 (vinculum notation) has a repeated block length of 1. It is also represented as 12.13999... (ellipsis notation) which equals approximately 12.1399999 (decimal approximation)(*).

The recurring decimal 12.139 can be written as a ratio of two integers having 607 as the numerator and 50 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.