What is 2.52222... as a Fraction?

2.522 equals 22790 as a fraction.

How do you turn 2.522 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.522 repeating into a fraction, begin writing this simple equation:

n = 2.522 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 2 digits in the non-repeating part (52). Multiply both sides by 10³ = 1000.

1000 × n = 2522.2 (equation 2)

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

1000 × n = 2522.2
 100 × n = 2.522
 900 × n = 2270

2270900 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 10 (the GCF - greatest common factor).

n = 2270900 = 2270 ÷ 10900 ÷ 10 = 22790. So,

2.522 = 22790 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 22790 is also equal to 24790 when expressed as a mixed number.

The repeating decimal 2.522 (vinculum notation) has a repeated block length of 1. It is also represented as 2.52222... (ellipsis notation) which equals approximately 2.5222222 (decimal approximation)(*).

The recurring decimal 2.522 can be written as a ratio of two integers having 227 as the numerator and 90 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.