What is 17.101222... as a Fraction?

17.1012 equals 1539119000 as a fraction.

How do you turn 17.1012 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.1012 repeating into a fraction, begin writing this simple equation:

n = 17.1012 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 3 digits in the non-repeating part (101). Multiply both sides by 10⁴ = 10000.

10000 × n = 171012.2 (equation 2)

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

10000 × n = 171012.2
 1000 × n = 17.1012
 9000 × n = 153911

n = 1539119000 (answer)

17.1012 = 1539119000 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 1539119000 is also equal to 179119000 when expressed as a mixed number.

The repeating decimal 17.1012 (vinculum notation) has a repeated block length of 1. It is also represented as 17.101222... (ellipsis notation) which equals approximately 17.10122222 (decimal approximation)(*).

The recurring decimal 17.1012 can be written as a ratio of two integers having 153911 as the numerator and 9000 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.