What is 12.75454... as a Fraction?

12.754 equals 1403110 as a fraction.

How do you turn 12.754 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.754 repeating into a fraction, begin writing this simple equation:

n = 12.754 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (54) and 1 digit in the non-repeating part (7). Multiply both sides by 10³ = 1000.

1000 × n = 12754.54 (equation 2)

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

1000 × n = 12754.54
  10 × n = 12.754
 990 × n = 12627

12627990 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 9 (the GCF - greatest common factor).

n = 12627990 = 12627 ÷ 9990 ÷ 9 = 1403110. So,

12.754 = 1403110 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 1403110 is also equal to 1283110 when expressed as a mixed number.

The repeating decimal 12.754 (vinculum notation) has a repeated block length of 2. It is also represented as 12.7545454... (ellipsis notation) which equals approximately 12.75454545454 (decimal approximation)(*).

The recurring decimal 12.754 can be written as a ratio of two integers having 1403 as the numerator and 110 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.