What is 0.291616... as a Fraction?

0.2916 equals 28879900 as a fraction.

How do you turn 0.2916 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.2916 repeating into a fraction, begin writing this simple equation:

n = 0.2916 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (16) and 2 digits in the non-repeating part (29). Multiply both sides by 10⁴ = 10000.

10000 × n = 2916.16 (equation 2)

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

10000 × n = 2916.16
  100 × n = 0.2916
 9900 × n = 2887

n = 28879900 (answer)

0.2916 = 28879900 as the lowest possible fraction.

The repeating decimal 0.2916 (vinculum notation) has a repeated block length of 2. It is also represented as 0.29161616... (ellipsis notation) which equals approximately 0.291616161616 (decimal approximation)(*).

The recurring decimal 0.2916 can be written as a ratio of two integers having 2887 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.