What is 10.1285285285... as a Fraction?

10.1285 equals 168641665 as a fraction.

How do you turn 10.1285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.1285 repeating into a fraction, begin writing this simple equation:

n = 10.1285 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (285) and 1 digit in the non-repeating part (1). Multiply both sides by 10⁴ = 10000.

10000 × n = 101285.285 (equation 2)

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

10000 × n = 101285.285
   10 × n = 10.1285
 9990 × n = 101184

1011849990 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 6 (the GCF - greatest common factor).

n = 1011849990 = 101184 ÷ 69990 ÷ 6 = 168641665. So,

10.1285 = 168641665 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 168641665 is also equal to 102141665 when expressed as a mixed number.

The repeating decimal 10.1285 (vinculum notation) has a repeated block length of 3. It is also represented as 10.1285285285... (ellipsis notation) which equals approximately 10.1285285285285285 (decimal approximation)(*).

The recurring decimal 10.1285 can be written as a ratio of two integers having 16864 as the numerator and 1665 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.