What is 17.006060606... as a Fraction?

17.06 equals 2806165 as a fraction.

How do you turn 17.06 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.06 repeating into a fraction, begin writing this simple equation:

n = 17.06 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (06), so multiply both sides by 10² = 100.

100 × n = 1706.06 (equation 2)

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

100 × n = 1706.06
  1 × n = 17.06
 99 × n = 1689

168999 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 = 168999 = 1689 ÷ 399 ÷ 3 = 2806165. So,

17.06 = 2806165 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 2806165 is also equal to 171165 when expressed as a mixed number.

The repeating decimal 17.06 (vinculum notation) has a repeated block length of 2. It is also represented as 17.060606... (ellipsis notation) which equals approximately 17.0606060606 (decimal approximation)(*).

The recurring decimal 17.06 can be written as a ratio of two integers having 2806 as the numerator and 165 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.