What is 2.113333... as a Fraction?

2.1133 equals 317150 as a fraction.

How do you turn 2.1133 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.1133 repeating into a fraction, begin writing this simple equation:

n = 2.1133 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 3 digits in the non-repeating part (113). Multiply both sides by 10⁴ = 10000.

10000 × n = 21133.3 (equation 2)

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

10000 × n = 21133.3
 1000 × n = 2.1133
 9000 × n = 19020

190209000 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 60 (the GCF - greatest common factor).

n = 190209000 = 19020 ÷ 609000 ÷ 60 = 317150. So,

2.1133 = 317150 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 317150 is also equal to 217150 when expressed as a mixed number.

The repeating decimal 2.1133 (vinculum notation) has a repeated block length of 1. It is also represented as 2.113333... (ellipsis notation) which equals approximately 2.11333333 (decimal approximation)(*).

The recurring decimal 2.1133 can be written as a ratio of two integers having 317 as the numerator and 150 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.