What is 0.86444... as a Fraction?

0.864 equals 389450 as a fraction.

How do you turn 0.864 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.864 repeating into a fraction, begin writing this simple equation:

n = 0.864 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (4) and 2 digits in the non-repeating part (86). Multiply both sides by 10³ = 1000.

1000 × n = 864.4 (equation 2)

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

1000 × n = 864.4
 100 × n = 0.864
 900 × n = 778

778900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 2 (the GCF - greatest common factor).

n = 778900 = 778 ÷ 2900 ÷ 2 = 389450. So,

0.864 = 389450 as the lowest possible fraction.

The repeating decimal 0.864 (vinculum notation) has a repeated block length of 1. It is also represented as 0.86444... (ellipsis notation) which equals approximately 0.8644444 (decimal approximation)(*).

The recurring decimal 0.864 can be written as a ratio of two integers having 389 as the numerator and 450 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.