What is 0.151616161616... as a Fraction?

0.1516 equals 15019900 as a fraction.

How do you turn 0.1516 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1516 repeating into a fraction, begin writing this simple equation:

n = 0.1516 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (16) and 2 digits in the non-repeating part (15). Multiply both sides by 10⁴ = 10000.

10000 × n = 1516.16 (equation 2)

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

10000 × n = 1516.16
  100 × n = 0.1516
 9900 × n = 1501

n = 15019900 (answer)

0.1516 = 15019900 as the lowest possible fraction.

The repeating decimal 0.1516 (vinculum notation) has a repeated block length of 2. It is also represented as 0.15161616... (ellipsis notation) which equals approximately 0.151616161616 (decimal approximation)(*).

The recurring decimal 0.1516 can be written as a ratio of two integers having 1501 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.