What is 3.827272727... as a Fraction?

3.827 equals 421110 as a fraction.

How do you turn 3.827 repeating into a fraction?

Detailed Answer:

Step 1: To convert 3.827 repeating into a fraction, begin writing this simple equation:

n = 3.827 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (27) and 1 digit in the non-repeating part (8). Multiply both sides by 10³ = 1000.

1000 × n = 3827.27 (equation 2)

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

1000 × n = 3827.27
  10 × n = 3.827
 990 × n = 3789

3789990 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 9 (the GCF - greatest common factor).

n = 3789990 = 3789 ÷ 9990 ÷ 9 = 421110. So,

3.827 = 421110 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 421110 is also equal to 391110 when expressed as a mixed number.

The repeating decimal 3.827 (vinculum notation) has a repeated block length of 2. It is also represented as 3.8272727... (ellipsis notation) which equals approximately 3.82727272727 (decimal approximation)(*).

The recurring decimal 3.827 can be written as a ratio of two integers having 421 as the numerator and 110 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.