What is 52.2666... as a Fraction?

52.26 equals 78415 as a fraction.

How do you turn 52.26 repeating into a fraction?

Detailed Answer:

Step 1: To convert 52.26 repeating into a fraction, begin writing this simple equation:

n = 52.26 (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 = 5226.6 (equation 2)

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

100 × n = 5226.6
 10 × n = 52.26
 90 × n = 4704

470490 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 = 470490 = 4704 ÷ 690 ÷ 6 = 78415. So,

52.26 = 78415 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 78415 is also equal to 52415 when expressed as a mixed number.

The repeating decimal 52.26 (vinculum notation) has a repeated block length of 1. It is also represented as 52.2666... (ellipsis notation) which equals approximately 52.266666 (decimal approximation)(*).

The recurring decimal 52.26 can be written as a ratio of two integers having 784 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.