What is 17.270606... as a Fraction?

17.2706 equals 569933300 as a fraction.

How do you turn 17.2706 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.2706 repeating into a fraction, begin writing this simple equation:

n = 17.2706 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (06) and 2 digits in the non-repeating part (27). Multiply both sides by 10⁴ = 10000.

10000 × n = 172706.06 (equation 2)

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

10000 × n = 172706.06
  100 × n = 17.2706
 9900 × n = 170979

1709799900 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 = 1709799900 = 170979 ÷ 39900 ÷ 3 = 569933300. So,

17.2706 = 569933300 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 569933300 is also equal to 178933300 when expressed as a mixed number.

The repeating decimal 17.2706 (vinculum notation) has a repeated block length of 2. It is also represented as 17.27060606... (ellipsis notation) which equals approximately 17.270606060606 (decimal approximation)(*).

The recurring decimal 17.2706 can be written as a ratio of two integers having 56993 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.