What is 13.428428428... as a Fraction?

13.428 equals 13415999 as a fraction.

How do you turn 13.428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.428 repeating into a fraction, begin writing this simple equation:

n = 13.428 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (428), so multiply both sides by 10³ = 1000.

1000 × n = 13428.428 (equation 2)

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

1000 × n = 13428.428
   1 × n = 13.428
 999 × n = 13415

n = 13415999 (answer)

13.428 = 13415999 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 13415999 is also equal to 13428999 when expressed as a mixed number.

The repeating decimal 13.428 (vinculum notation) has a repeated block length of 3. It is also represented as 13.428428428... (ellipsis notation) which equals approximately 13.428428428428428 (decimal approximation)(*).

The recurring decimal 13.428 can be written as a ratio of two integers having 13415 as the numerator and 999 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.