What is 0.62888... as a Fraction?

0.628 equals 283450 as a fraction.

How do you turn 0.628 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.628 repeating into a fraction, begin writing this simple equation:

n = 0.628 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (62). Multiply both sides by 10³ = 1000.

1000 × n = 628.8 (equation 2)

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

1000 × n = 628.8
 100 × n = 0.628
 900 × n = 566

566900 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 = 566900 = 566 ÷ 2900 ÷ 2 = 283450. So,

0.628 = 283450 as the lowest possible fraction.

The repeating decimal 0.628 (vinculum notation) has a repeated block length of 1. It is also represented as 0.62888... (ellipsis notation) which equals approximately 0.6288888 (decimal approximation)(*).

The recurring decimal 0.628 can be written as a ratio of two integers having 283 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.