What is 1.1902020202... as a Fraction?

1.1902 equals 117839900 as a fraction.

How do you turn 1.1902 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.1902 repeating into a fraction, begin writing this simple equation:

n = 1.1902 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (02) and 2 digits in the non-repeating part (19). Multiply both sides by 10⁴ = 10000.

10000 × n = 11902.02 (equation 2)

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

10000 × n = 11902.02
  100 × n = 1.1902
 9900 × n = 11783

n = 117839900 (answer)

1.1902 = 117839900 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 117839900 is also equal to 118839900 when expressed as a mixed number.

The repeating decimal 1.1902 (vinculum notation) has a repeated block length of 2. It is also represented as 1.19020202... (ellipsis notation) which equals approximately 1.190202020202 (decimal approximation)(*).

The recurring decimal 1.1902 can be written as a ratio of two integers having 11783 as the numerator and 9900 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.