What is 13.0142142142... as a Fraction?

13.142 equals 650064995 as a fraction.

How do you turn 13.142 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.142 repeating into a fraction, begin writing this simple equation:

n = 13.142 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (142), so multiply both sides by 10³ = 1000.

1000 × n = 13142.142 (equation 2)

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

1000 × n = 13142.142
   1 × n = 13.142
 999 × n = 13129

n = 650064995 (answer)

13.142 = 650064995 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 650064995 is also equal to 13714995 when expressed as a mixed number.

The repeating decimal 13.142 (vinculum notation) has a repeated block length of 3. It is also represented as 13.142142142... (ellipsis notation) which equals approximately 13.142142142142142 (decimal approximation)(*).

The recurring decimal 13.142 can be written as a ratio of two integers having 65006 as the numerator and 4995 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.