What is 23.125454... as a Fraction?

23.1254 equals 12719550 as a fraction.

How do you turn 23.1254 repeating into a fraction?

Detailed Answer:

Step 1: To convert 23.1254 repeating into a fraction, begin writing this simple equation:

n = 23.1254 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (54) and 2 digits in the non-repeating part (12). Multiply both sides by 10⁴ = 10000.

10000 × n = 231254.54 (equation 2)

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

10000 × n = 231254.54
  100 × n = 23.1254
 9900 × n = 228942

2289429900 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 18 (the GCF - greatest common factor).

n = 2289429900 = 228942 ÷ 189900 ÷ 18 = 12719550. So,

23.1254 = 12719550 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 12719550 is also equal to 2369550 when expressed as a mixed number.

The repeating decimal 23.1254 (vinculum notation) has a repeated block length of 2. It is also represented as 23.12545454... (ellipsis notation) which equals approximately 23.125454545454 (decimal approximation)(*).

The recurring decimal 23.1254 can be written as a ratio of two integers having 12719 as the numerator and 550 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.