What is 10.2676767... as a Fraction?

10.267 equals 2033198 as a fraction.

How do you turn 10.267 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.267 repeating into a fraction, begin writing this simple equation:

n = 10.267 (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 = 10267.67 (equation 2)

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

1000 × n = 10267.67
  10 × n = 10.267
 990 × n = 10165

10165990 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 = 10165990 = 10165 ÷ 5990 ÷ 5 = 2033198. So,

10.267 = 2033198 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 2033198 is also equal to 1053198 when expressed as a mixed number.

The repeating decimal 10.267 (vinculum notation) has a repeated block length of 2. It is also represented as 10.2676767... (ellipsis notation) which equals approximately 10.26767676767 (decimal approximation)(*).

The recurring decimal 10.267 can be written as a ratio of two integers having 2033 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.