What is 4.281428142814281428... as a Fraction?

4.281428 equals 142703333 as a fraction.

How do you turn 4.281428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.281428 repeating into a fraction, begin writing this simple equation:

n = 4.281428 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (1428) and 2 digits in the non-repeating part (28). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 4281428.1428 (equation 2)

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

1000000 × n = 4281428.1428
    100 × n = 4.281428
 999900 × n = 4281000

4281000999900 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 300 (the GCF - greatest common factor).

n = 4281000999900 = 4281000 ÷ 300999900 ÷ 300 = 142703333. So,

4.281428 = 142703333 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 142703333 is also equal to 49383333 when expressed as a mixed number.

The repeating decimal 4.281428 (vinculum notation) has a repeated block length of 4. It is also represented as 4.28142814281428... (ellipsis notation) which equals approximately 4.2814281428142814281428 (decimal approximation)(*).

The recurring decimal 4.281428 can be written as a ratio of two integers having 14270 as the numerator and 3333 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.