What is 17.209090... as a Fraction?

17.2090 equals 1893110 as a fraction.

How do you turn 17.2090 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.2090 repeating into a fraction, begin writing this simple equation:

n = 17.2090 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (90) and 2 digits in the non-repeating part (20). Multiply both sides by 10⁴ = 10000.

10000 × n = 172090.90 (equation 2)

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

10000 × n = 172090.90
  100 × n = 17.2090
 9900 × n = 170370

1703709900 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 90 (the GCF - greatest common factor).

n = 1703709900 = 170370 ÷ 909900 ÷ 90 = 1893110. So,

17.2090 = 1893110 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 1893110 is also equal to 1723110 when expressed as a mixed number.

The repeating decimal 17.2090 (vinculum notation) has a repeated block length of 2. It is also represented as 17.20909090... (ellipsis notation) which equals approximately 17.209090909090 (decimal approximation)(*).

The recurring decimal 17.2090 can be written as a ratio of two integers having 1893 as the numerator and 110 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.