What is 0.103666... as a Fraction?

0.1036 equals 3113000 as a fraction.

How do you turn 0.1036 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1036 repeating into a fraction, begin writing this simple equation:

n = 0.1036 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 3 digits in the non-repeating part (103). Multiply both sides by 10⁴ = 10000.

10000 × n = 1036.6 (equation 2)

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

10000 × n = 1036.6
 1000 × n = 0.1036
 9000 × n = 933

9339000 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 3 (the GCF - greatest common factor).

n = 9339000 = 933 ÷ 39000 ÷ 3 = 3113000. So,

0.1036 = 3113000 as the lowest possible fraction.

The repeating decimal 0.1036 (vinculum notation) has a repeated block length of 1. It is also represented as 0.103666... (ellipsis notation) which equals approximately 0.10366666 (decimal approximation)(*).

The recurring decimal 0.1036 can be written as a ratio of two integers having 311 as the numerator and 3000 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.