What is 14.48571485714857148571485714... as a Fraction?

14.485714 equals 144855799999 as a fraction.

How do you turn 14.485714 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.485714 repeating into a fraction, begin writing this simple equation:

n = 14.485714 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (85714) and 1 digit in the non-repeating part (4). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 14485714.85714 (equation 2)

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

1000000 × n = 14485714.85714
     10 × n = 14.485714
 999990 × n = 14485570

14485570999990 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 10 (the GCF - greatest common factor).

n = 14485570999990 = 14485570 ÷ 10999990 ÷ 10 = 144855799999. So,

14.485714 = 144855799999 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 144855799999 is also equal to 144857199999 when expressed as a mixed number.

The repeating decimal 14.485714 (vinculum notation) has a repeated block length of 5. It is also represented as 14.4857148571485714... (ellipsis notation) which equals approximately 14.48571485714857148571485714 (decimal approximation)(*).

The recurring decimal 14.485714 can be written as a ratio of two integers having 1448557 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.