What is 23.490909090... as a Fraction?

23.490 equals 129255 as a fraction.

How do you turn 23.490 repeating into a fraction?

Detailed Answer:

Step 1: To convert 23.490 repeating into a fraction, begin writing this simple equation:

n = 23.490 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (90) and 1 digit in the non-repeating part (4). Multiply both sides by 10³ = 1000.

1000 × n = 23490.90 (equation 2)

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

1000 × n = 23490.90
  10 × n = 23.490
 990 × n = 23256

23256990 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 = 23256990 = 23256 ÷ 18990 ÷ 18 = 129255. So,

23.490 = 129255 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 129255 is also equal to 232755 when expressed as a mixed number.

The repeating decimal 23.490 (vinculum notation) has a repeated block length of 2. It is also represented as 23.4909090... (ellipsis notation) which equals approximately 23.49090909090 (decimal approximation)(*).

The recurring decimal 23.490 can be written as a ratio of two integers having 1292 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.