What is 2.68666... as a Fraction?

2.686 equals 403150 as a fraction.

How do you turn 2.686 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.686 repeating into a fraction, begin writing this simple equation:

n = 2.686 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (68). Multiply both sides by 10³ = 1000.

1000 × n = 2686.6 (equation 2)

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

1000 × n = 2686.6
 100 × n = 2.686
 900 × n = 2418

2418900 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 6 (the GCF - greatest common factor).

n = 2418900 = 2418 ÷ 6900 ÷ 6 = 403150. So,

2.686 = 403150 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 403150 is also equal to 2103150 when expressed as a mixed number.

The repeating decimal 2.686 (vinculum notation) has a repeated block length of 1. It is also represented as 2.68666... (ellipsis notation) which equals approximately 2.6866666 (decimal approximation)(*).

The recurring decimal 2.686 can be written as a ratio of two integers having 403 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.