What is 16.1306060606... as a Fraction?

16.1306 equals 532313300 as a fraction.

How do you turn 16.1306 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.1306 repeating into a fraction, begin writing this simple equation:

n = 16.1306 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (06) and 2 digits in the non-repeating part (13). Multiply both sides by 10⁴ = 10000.

10000 × n = 161306.06 (equation 2)

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

10000 × n = 161306.06
  100 × n = 16.1306
 9900 × n = 159693

1596939900 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 = 1596939900 = 159693 ÷ 39900 ÷ 3 = 532313300. So,

16.1306 = 532313300 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 532313300 is also equal to 164313300 when expressed as a mixed number.

The repeating decimal 16.1306 (vinculum notation) has a repeated block length of 2. It is also represented as 16.13060606... (ellipsis notation) which equals approximately 16.130606060606 (decimal approximation)(*).

The recurring decimal 16.1306 can be written as a ratio of two integers having 53231 as the numerator and 3300 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.