What is 23.145454... as a Fraction?

23.1454 equals 127355 as a fraction.

How do you turn 23.1454 repeating into a fraction?

Detailed Answer:

Step 1: To convert 23.1454 repeating into a fraction, begin writing this simple equation:

n = 23.1454 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (54) and 2 digits in the non-repeating part (14). Multiply both sides by 10⁴ = 10000.

10000 × n = 231454.54 (equation 2)

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

10000 × n = 231454.54
  100 × n = 23.1454
 9900 × n = 229140

2291409900 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 180 (the GCF - greatest common factor).

n = 2291409900 = 229140 ÷ 1809900 ÷ 180 = 127355. So,

23.1454 = 127355 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 127355 is also equal to 23855 when expressed as a mixed number.

The repeating decimal 23.1454 (vinculum notation) has a repeated block length of 2. It is also represented as 23.14545454... (ellipsis notation) which equals approximately 23.145454545454 (decimal approximation)(*).

The recurring decimal 23.1454 can be written as a ratio of two integers having 1273 as the numerator and 55 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.