What is 23.18333... as a Fraction?

23.183 equals 139160 as a fraction.

How do you turn 23.183 repeating into a fraction?

Detailed Answer:

Step 1: To convert 23.183 repeating into a fraction, begin writing this simple equation:

n = 23.183 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (18). Multiply both sides by 10³ = 1000.

1000 × n = 23183.3 (equation 2)

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

1000 × n = 23183.3
 100 × n = 23.183
 900 × n = 20865

20865900 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 15 (the GCF - greatest common factor).

n = 20865900 = 20865 ÷ 15900 ÷ 15 = 139160. So,

23.183 = 139160 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 139160 is also equal to 231160 when expressed as a mixed number.

The repeating decimal 23.183 (vinculum notation) has a repeated block length of 1. It is also represented as 23.18333... (ellipsis notation) which equals approximately 23.1833333 (decimal approximation)(*).

The recurring decimal 23.183 can be written as a ratio of two integers having 1391 as the numerator and 60 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.