What is 4.54285428542854285... as a Fraction?

4.54285 equals 454249999 as a fraction.

How do you turn 4.54285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.54285 repeating into a fraction, begin writing this simple equation:

n = 4.54285 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (4285) and 1 digit in the non-repeating part (5). Multiply both sides by 10⁵ = 100000.

100000 × n = 454285.4285 (equation 2)

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

100000 × n = 454285.4285
    10 × n = 4.54285
 99990 × n = 454240

45424099990 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 = 45424099990 = 454240 ÷ 1099990 ÷ 10 = 454249999. So,

4.54285 = 454249999 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 454249999 is also equal to 454289999 when expressed as a mixed number.

The repeating decimal 4.54285 (vinculum notation) has a repeated block length of 4. It is also represented as 4.5428542854285... (ellipsis notation) which equals approximately 4.542854285428542854285 (decimal approximation)(*).

The recurring decimal 4.54285 can be written as a ratio of two integers having 45424 as the numerator and 9999 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.