What is 15.116222... as a Fraction?

15.1162 equals 680234500 as a fraction.

How do you turn 15.1162 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.1162 repeating into a fraction, begin writing this simple equation:

n = 15.1162 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 3 digits in the non-repeating part (116). Multiply both sides by 10⁴ = 10000.

10000 × n = 151162.2 (equation 2)

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

10000 × n = 151162.2
 1000 × n = 15.1162
 9000 × n = 136046

1360469000 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 2 (the GCF - greatest common factor).

n = 1360469000 = 136046 ÷ 29000 ÷ 2 = 680234500. So,

15.1162 = 680234500 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 680234500 is also equal to 155234500 when expressed as a mixed number.

The repeating decimal 15.1162 (vinculum notation) has a repeated block length of 1. It is also represented as 15.116222... (ellipsis notation) which equals approximately 15.11622222 (decimal approximation)(*).

The recurring decimal 15.1162 can be written as a ratio of two integers having 68023 as the numerator and 4500 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.