What is 2.001010101... as a Fraction?

2.01 equals 1981990 as a fraction.

How do you turn 2.01 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.01 repeating into a fraction, begin writing this simple equation:

n = 2.01 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (01), so multiply both sides by 10² = 100.

100 × n = 201.01 (equation 2)

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

100 × n = 201.01
  1 × n = 2.01
 99 × n = 199

n = 1981990 (answer)

2.01 = 1981990 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 1981990 is also equal to 21990 when expressed as a mixed number.

The repeating decimal 2.01 (vinculum notation) has a repeated block length of 2. It is also represented as 2.010101... (ellipsis notation) which equals approximately 2.0101010101 (decimal approximation)(*).

The recurring decimal 2.01 can be written as a ratio of two integers having 1981 as the numerator and 990 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.