What is 15.16666... as a Fraction?

15.166 equals 916 as a fraction.

How do you turn 15.166 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.166 repeating into a fraction, begin writing this simple equation:

n = 15.166 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (16). Multiply both sides by 10³ = 1000.

1000 × n = 15166.6 (equation 2)

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

1000 × n = 15166.6
 100 × n = 15.166
 900 × n = 13650

13650900 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 150 (the GCF - greatest common factor).

n = 13650900 = 13650 ÷ 150900 ÷ 150 = 916. So,

15.166 = 916 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 916 is also equal to 1516 when expressed as a mixed number.

The repeating decimal 15.166 (vinculum notation) has a repeated block length of 1. It is also represented as 15.16666... (ellipsis notation) which equals approximately 15.1666666 (decimal approximation)(*).

The recurring decimal 15.166 can be written as a ratio of two integers having 91 as the numerator and 6 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.