What is 0.000111... as a Fraction?

0.0001 equals 19000 as a fraction.

How do you turn 0.0001 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.0001 repeating into a fraction, begin writing this simple equation:

n = 0.0001 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (1) and 3 digits in the non-repeating part (000). Multiply both sides by 10⁴ = 10000.

10000 × n = 1.1 (equation 2)

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

10000 × n = 1.1
 1000 × n = 0.0001
 9000 × n = 1

n = 19000 (answer)

0.0001 = 19000 as the lowest possible fraction.

The repeating decimal 0.0001 (vinculum notation) has a repeated block length of 1. It is also represented as 0.000111... (ellipsis notation) which equals approximately 0.00011111 (decimal approximation)(*).

The recurring decimal 0.0001 can be written as a ratio of two integers having 1 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.