What is 10.1428514285142851428514285... as a Fraction?

10.14285 equals 101427599999 as a fraction.

How do you turn 10.14285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.14285 repeating into a fraction, begin writing this simple equation:

n = 10.14285 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (14285), so multiply both sides by 10⁵ = 100000.

100000 × n = 1014285.14285 (equation 2)

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

100000 × n = 1014285.14285
     1 × n = 10.14285
 99999 × n = 1014275

n = 101427599999 (answer)

10.14285 = 101427599999 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 101427599999 is also equal to 101428599999 when expressed as a mixed number.

The repeating decimal 10.14285 (vinculum notation) has a repeated block length of 5. It is also represented as 10.142851428514285... (ellipsis notation) which equals approximately 10.1428514285142851428514285 (decimal approximation)(*).

The recurring decimal 10.14285 can be written as a ratio of two integers having 1014275 as the numerator and 99999 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.