What is 0.9999... as a Fraction?

0.9 equals 11 as a fraction.

How do you turn 0.9 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.9 repeating into a fraction, begin writing this simple equation:

n = 0.9 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (9), so multiply both sides by 10¹ = 10.

10 × n = 9.9 (equation 2)

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

10 × n = 9.9
 1 × n = 0.9
 9 × n = 9

99 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 9 (the GCF - greatest common factor).

n = 99 = 9 ÷ 99 ÷ 9 = 11. So,

0.9 = 11 as the lowest possible fraction.

The repeating decimal 0.9 (vinculum notation) has a repeated block length of 1. It is also represented as 0.999... (ellipsis notation) which equals approximately 0.99999 (decimal approximation)(*).

The recurring decimal 0.9 can be written as a ratio of two integers having 1 as the numerator and 1 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.