What is 12.153153153... as a Fraction?

12.153 equals 1349111 as a fraction.

How do you turn 12.153 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.153 repeating into a fraction, begin writing this simple equation:

n = 12.153 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (153), so multiply both sides by 10³ = 1000.

1000 × n = 12153.153 (equation 2)

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

1000 × n = 12153.153
   1 × n = 12.153
 999 × n = 12141

12141999 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 = 12141999 = 12141 ÷ 9999 ÷ 9 = 1349111. So,

12.153 = 1349111 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 1349111 is also equal to 1217111 when expressed as a mixed number.

The repeating decimal 12.153 (vinculum notation) has a repeated block length of 3. It is also represented as 12.153153153... (ellipsis notation) which equals approximately 12.153153153153153 (decimal approximation)(*).

The recurring decimal 12.153 can be written as a ratio of two integers having 1349 as the numerator and 111 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.