What is 0.72828... as a Fraction?

0.728 equals 721990 as a fraction.

How do you turn 0.728 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.728 repeating into a fraction, begin writing this simple equation:

n = 0.728 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (28) and 1 digit in the non-repeating part (7). Multiply both sides by 10³ = 1000.

1000 × n = 728.28 (equation 2)

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

1000 × n = 728.28
  10 × n = 0.728
 990 × n = 721

n = 721990 (answer)

0.728 = 721990 as the lowest possible fraction.

The repeating decimal 0.728 (vinculum notation) has a repeated block length of 2. It is also represented as 0.7282828... (ellipsis notation) which equals approximately 0.72828282828 (decimal approximation)(*).

The recurring decimal 0.728 can be written as a ratio of two integers having 721 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.