What is 0.57888... as a Fraction?

0.578 equals 521900 as a fraction.

How do you turn 0.578 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.578 repeating into a fraction, begin writing this simple equation:

n = 0.578 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (57). Multiply both sides by 10³ = 1000.

1000 × n = 578.8 (equation 2)

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

1000 × n = 578.8
 100 × n = 0.578
 900 × n = 521

n = 521900 (answer)

0.578 = 521900 as the lowest possible fraction.

The repeating decimal 0.578 (vinculum notation) has a repeated block length of 1. It is also represented as 0.57888... (ellipsis notation) which equals approximately 0.5788888 (decimal approximation)(*).

The recurring decimal 0.578 can be written as a ratio of two integers having 521 as the numerator and 900 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.