What is 0.110101... as a Fraction?

0.1101 equals 109990 as a fraction.

How do you turn 0.1101 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1101 repeating into a fraction, begin writing this simple equation:

n = 0.1101 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (01) and 2 digits in the non-repeating part (11). Multiply both sides by 10⁴ = 10000.

10000 × n = 1101.01 (equation 2)

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

10000 × n = 1101.01
  100 × n = 0.1101
 9900 × n = 1090

10909900 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 10 (the GCF - greatest common factor).

n = 10909900 = 1090 ÷ 109900 ÷ 10 = 109990. So,

0.1101 = 109990 as the lowest possible fraction.

The repeating decimal 0.1101 (vinculum notation) has a repeated block length of 2. It is also represented as 0.11010101... (ellipsis notation) which equals approximately 0.110101010101 (decimal approximation)(*).

The recurring decimal 0.1101 can be written as a ratio of two integers having 109 as the numerator and 990 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.