What is 21.0571571571... as a Fraction?

21.571 equals 2103619990 as a fraction.

How do you turn 21.571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 21.571 repeating into a fraction, begin writing this simple equation:

n = 21.571 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (571), so multiply both sides by 10³ = 1000.

1000 × n = 21571.571 (equation 2)

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

1000 × n = 21571.571
   1 × n = 21.571
 999 × n = 21550

n = 2103619990 (answer)

21.571 = 2103619990 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 2103619990 is also equal to 215719990 when expressed as a mixed number.

The repeating decimal 21.571 (vinculum notation) has a repeated block length of 3. It is also represented as 21.571571571... (ellipsis notation) which equals approximately 21.571571571571571 (decimal approximation)(*).

The recurring decimal 21.571 can be written as a ratio of two integers having 210361 as the numerator and 9990 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.