What is 10.1428142814281428... as a Fraction?

10.1428 equals 338063333 as a fraction.

How do you turn 10.1428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.1428 repeating into a fraction, begin writing this simple equation:

n = 10.1428 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (1428), so multiply both sides by 10⁴ = 10000.

10000 × n = 101428.1428 (equation 2)

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

10000 × n = 101428.1428
    1 × n = 10.1428
 9999 × n = 101418

1014189999 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 3 (the GCF - greatest common factor).

n = 1014189999 = 101418 ÷ 39999 ÷ 3 = 338063333. So,

10.1428 = 338063333 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 338063333 is also equal to 104763333 when expressed as a mixed number.

The repeating decimal 10.1428 (vinculum notation) has a repeated block length of 4. It is also represented as 10.142814281428... (ellipsis notation) which equals approximately 10.14281428142814281428 (decimal approximation)(*).

The recurring decimal 10.1428 can be written as a ratio of two integers having 33806 as the numerator and 3333 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.