What is 23.18999... as a Fraction?

23.189 equals 2319100 as a fraction.

How do you turn 23.189 repeating into a fraction?

Detailed Answer:

Step 1: To convert 23.189 repeating into a fraction, begin writing this simple equation:

n = 23.189 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (9) and 2 digits in the non-repeating part (18). Multiply both sides by 10³ = 1000.

1000 × n = 23189.9 (equation 2)

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

1000 × n = 23189.9
 100 × n = 23.189
 900 × n = 20871

20871900 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 9 (the GCF - greatest common factor).

n = 20871900 = 20871 ÷ 9900 ÷ 9 = 2319100. So,

23.189 = 2319100 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 2319100 is also equal to 2319100 when expressed as a mixed number.

The repeating decimal 23.189 (vinculum notation) has a repeated block length of 1. It is also represented as 23.18999... (ellipsis notation) which equals approximately 23.1899999 (decimal approximation)(*).

The recurring decimal 23.189 can be written as a ratio of two integers having 2319 as the numerator and 100 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.