What is 14.55757... as a Fraction?

14.557 equals 2402165 as a fraction.

How do you turn 14.557 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.557 repeating into a fraction, begin writing this simple equation:

n = 14.557 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (57) and 1 digit in the non-repeating part (5). Multiply both sides by 10³ = 1000.

1000 × n = 14557.57 (equation 2)

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

1000 × n = 14557.57
  10 × n = 14.557
 990 × n = 14412

14412990 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 = 14412990 = 14412 ÷ 6990 ÷ 6 = 2402165. So,

14.557 = 2402165 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 2402165 is also equal to 1492165 when expressed as a mixed number.

The repeating decimal 14.557 (vinculum notation) has a repeated block length of 2. It is also represented as 14.5575757... (ellipsis notation) which equals approximately 14.55757575757 (decimal approximation)(*).

The recurring decimal 14.557 can be written as a ratio of two integers having 2402 as the numerator and 165 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.