What is 0.01616... as a Fraction?

0.16 equals 8495 as a fraction.

How do you turn 0.16 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.16 repeating into a fraction, begin writing this simple equation:

n = 0.16 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (16), so multiply both sides by 10² = 100.

100 × n = 16.16 (equation 2)

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

100 × n = 16.16
  1 × n = 0.16
 99 × n = 16

n = 8495 (answer)

0.16 = 8495 as the lowest possible fraction.

The repeating decimal 0.16 (vinculum notation) has a repeated block length of 2. It is also represented as 0.161616... (ellipsis notation) which equals approximately 0.1616161616 (decimal approximation)(*).

The recurring decimal 0.16 can be written as a ratio of two integers having 8 as the numerator and 495 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.