What is 23.06060606... as a Fraction?

23.06 equals 76133 as a fraction.

How do you turn 23.06 repeating into a fraction?

Detailed Answer:

Step 1: To convert 23.06 repeating into a fraction, begin writing this simple equation:

n = 23.06 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (06), so multiply both sides by 10² = 100.

100 × n = 2306.06 (equation 2)

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

100 × n = 2306.06
  1 × n = 23.06
 99 × n = 2283

228399 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 3 (the GCF - greatest common factor).

n = 228399 = 2283 ÷ 399 ÷ 3 = 76133. So,

23.06 = 76133 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 76133 is also equal to 23233 when expressed as a mixed number.

The repeating decimal 23.06 (vinculum notation) has a repeated block length of 2. It is also represented as 23.060606... (ellipsis notation) which equals approximately 23.0606060606 (decimal approximation)(*).

The recurring decimal 23.06 can be written as a ratio of two integers having 761 as the numerator and 33 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.