What is 99.111... as a Fraction?

99.1 equals 8929 as a fraction.

How do you turn 99.1 repeating into a fraction?

Detailed Answer:

Step 1: To convert 99.1 repeating into a fraction, begin writing this simple equation:

n = 99.1 (equation 1)

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

10 × n = 991.1 (equation 2)

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

10 × n = 991.1
 1 × n = 99.1
 9 × n = 892

n = 8929 (answer)

99.1 = 8929 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 8929 is also equal to 9919 when expressed as a mixed number.

The repeating decimal 99.1 (vinculum notation) has a repeated block length of 1. It is also represented as 99.111... (ellipsis notation) which equals approximately 99.11111 (decimal approximation)(*).

The recurring decimal 99.1 can be written as a ratio of two integers having 892 as the numerator and 9 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.