What is 15.66... as a Fraction?

15.6 equals 473 as a fraction.

How do you turn 15.6 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.6 repeating into a fraction, begin writing this simple equation:

n = 15.6 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6), so multiply both sides by 10¹ = 10.

10 × n = 156.6 (equation 2)

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

10 × n = 156.6
 1 × n = 15.6
 9 × n = 141

1419 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 3 (the GCF - greatest common factor).

n = 1419 = 141 ÷ 39 ÷ 3 = 473. So,

15.6 = 473 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 473 is also equal to 1523 when expressed as a mixed number.

The repeating decimal 15.6 (vinculum notation) has a repeated block length of 1. It is also represented as 15.666... (ellipsis notation) which equals approximately 15.66666 (decimal approximation)(*).

The recurring decimal 15.6 can be written as a ratio of two integers having 47 as the numerator and 3 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.