What is 67.2666... as a Fraction?

67.26 equals 100915 as a fraction.

How do you turn 67.26 repeating into a fraction?

Detailed Answer:

Step 1: To convert 67.26 repeating into a fraction, begin writing this simple equation:

n = 67.26 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 1 digit in the non-repeating part (2). Multiply both sides by 10² = 100.

100 × n = 6726.6 (equation 2)

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

100 × n = 6726.6
 10 × n = 67.26
 90 × n = 6054

605490 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 = 605490 = 6054 ÷ 690 ÷ 6 = 100915. So,

67.26 = 100915 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 100915 is also equal to 67415 when expressed as a mixed number.

The repeating decimal 67.26 (vinculum notation) has a repeated block length of 1. It is also represented as 67.2666... (ellipsis notation) which equals approximately 67.266666 (decimal approximation)(*).

The recurring decimal 67.26 can be written as a ratio of two integers having 1009 as the numerator and 15 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.