What is 14.13111... as a Fraction?

14.131 equals 6359450 as a fraction.

How do you turn 14.131 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.131 repeating into a fraction, begin writing this simple equation:

n = 14.131 (equation 1)

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

1000 × n = 14131.1 (equation 2)

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

1000 × n = 14131.1
 100 × n = 14.131
 900 × n = 12718

12718900 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 2 (the GCF - greatest common factor).

n = 12718900 = 12718 ÷ 2900 ÷ 2 = 6359450. So,

14.131 = 6359450 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 6359450 is also equal to 1459450 when expressed as a mixed number.

The repeating decimal 14.131 (vinculum notation) has a repeated block length of 1. It is also represented as 14.13111... (ellipsis notation) which equals approximately 14.1311111 (decimal approximation)(*).

The recurring decimal 14.131 can be written as a ratio of two integers having 6359 as the numerator and 450 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.