What is 1.571571571... as a Fraction?

1.571 equals 1570999 as a fraction.

How do you turn 1.571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.571 repeating into a fraction, begin writing this simple equation:

n = 1.571 (equation 1)

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

1000 × n = 1571.571 (equation 2)

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

1000 × n = 1571.571
   1 × n = 1.571
 999 × n = 1570

n = 1570999 (answer)

1.571 = 1570999 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 1570999 is also equal to 1571999 when expressed as a mixed number.

The repeating decimal 1.571 (vinculum notation) has a repeated block length of 3. It is also represented as 1.571571571... (ellipsis notation) which equals approximately 1.571571571571571 (decimal approximation)(*).

The recurring decimal 1.571 can be written as a ratio of two integers having 1570 as the numerator and 999 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.