What is 0.2676767... as a Fraction?

0.267 equals 53198 as a fraction.

How do you turn 0.267 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.267 repeating into a fraction, begin writing this simple equation:

n = 0.267 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (67) and 1 digit in the non-repeating part (2). Multiply both sides by 10³ = 1000.

1000 × n = 267.67 (equation 2)

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

1000 × n = 267.67
  10 × n = 0.267
 990 × n = 265

265990 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 5 (the GCF - greatest common factor).

n = 265990 = 265 ÷ 5990 ÷ 5 = 53198. So,

0.267 = 53198 as the lowest possible fraction.

The repeating decimal 0.267 (vinculum notation) has a repeated block length of 2. It is also represented as 0.2676767... (ellipsis notation) which equals approximately 0.26767676767 (decimal approximation)(*).

The recurring decimal 0.267 can be written as a ratio of two integers having 53 as the numerator and 198 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.