What is 0.109333... as a Fraction?

0.1093 equals 41375 as a fraction.

How do you turn 0.1093 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1093 repeating into a fraction, begin writing this simple equation:

n = 0.1093 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 3 digits in the non-repeating part (109). Multiply both sides by 10⁴ = 10000.

10000 × n = 1093.3 (equation 2)

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

10000 × n = 1093.3
 1000 × n = 0.1093
 9000 × n = 984

9849000 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 24 (the GCF - greatest common factor).

n = 9849000 = 984 ÷ 249000 ÷ 24 = 41375. So,

0.1093 = 41375 as the lowest possible fraction.

The repeating decimal 0.1093 (vinculum notation) has a repeated block length of 1. It is also represented as 0.109333... (ellipsis notation) which equals approximately 0.10933333 (decimal approximation)(*).

The recurring decimal 0.1093 can be written as a ratio of two integers having 41 as the numerator and 375 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.