What is 2.245454545... as a Fraction?

2.245 equals 247110 as a fraction.

How do you turn 2.245 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.245 repeating into a fraction, begin writing this simple equation:

n = 2.245 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (45) and 1 digit in the non-repeating part (2). Multiply both sides by 10³ = 1000.

1000 × n = 2245.45 (equation 2)

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

1000 × n = 2245.45
  10 × n = 2.245
 990 × n = 2223

2223990 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 9 (the GCF - greatest common factor).

n = 2223990 = 2223 ÷ 9990 ÷ 9 = 247110. So,

2.245 = 247110 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 247110 is also equal to 227110 when expressed as a mixed number.

The repeating decimal 2.245 (vinculum notation) has a repeated block length of 2. It is also represented as 2.2454545... (ellipsis notation) which equals approximately 2.24545454545 (decimal approximation)(*).

The recurring decimal 2.245 can be written as a ratio of two integers having 247 as the numerator and 110 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.