What is 0.10202... as a Fraction?

0.102 equals 101990 as a fraction.

How do you turn 0.102 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.102 repeating into a fraction, begin writing this simple equation:

n = 0.102 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (02) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 102.02 (equation 2)

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

1000 × n = 102.02
  10 × n = 0.102
 990 × n = 101

n = 101990 (answer)

0.102 = 101990 as the lowest possible fraction.

The repeating decimal 0.102 (vinculum notation) has a repeated block length of 2. It is also represented as 0.1020202... (ellipsis notation) which equals approximately 0.10202020202 (decimal approximation)(*).

The recurring decimal 0.102 can be written as a ratio of two integers having 101 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.