What is 11.151428514285142851428514285... as a Fraction?

11.1514285 equals 11151317999990 as a fraction.

How do you turn 11.1514285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1514285 repeating into a fraction, begin writing this simple equation:

n = 11.1514285 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (14285) and 2 digits in the non-repeating part (15). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 111514285.14285 (equation 2)

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

10000000 × n = 111514285.14285
     100 × n = 11.1514285
 9999900 × n = 111513170

1115131709999900 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 10 (the GCF - greatest common factor).

n = 1115131709999900 = 111513170 ÷ 109999900 ÷ 10 = 11151317999990. So,

11.1514285 = 11151317999990 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 11151317999990 is also equal to 11151427999990 when expressed as a mixed number.

The repeating decimal 11.1514285 (vinculum notation) has a repeated block length of 5. It is also represented as 11.15142851428514285... (ellipsis notation) which equals approximately 11.151428514285142851428514285 (decimal approximation)(*).

The recurring decimal 11.1514285 can be written as a ratio of two integers having 11151317 as the numerator and 999990 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.