What is 2.74242... as a Fraction?

2.742 equals 18166 as a fraction.

How do you turn 2.742 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.742 repeating into a fraction, begin writing this simple equation:

n = 2.742 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (42) and 1 digit in the non-repeating part (7). Multiply both sides by 10³ = 1000.

1000 × n = 2742.42 (equation 2)

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

1000 × n = 2742.42
  10 × n = 2.742
 990 × n = 2715

2715990 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 15 (the GCF - greatest common factor).

n = 2715990 = 2715 ÷ 15990 ÷ 15 = 18166. So,

2.742 = 18166 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 18166 is also equal to 24966 when expressed as a mixed number.

The repeating decimal 2.742 (vinculum notation) has a repeated block length of 2. It is also represented as 2.7424242... (ellipsis notation) which equals approximately 2.74242424242 (decimal approximation)(*).

The recurring decimal 2.742 can be written as a ratio of two integers having 181 as the numerator and 66 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.