What is 5.38428428428... as a Fraction?

5.38428 equals 537899990 as a fraction.

How do you turn 5.38428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 5.38428 repeating into a fraction, begin writing this simple equation:

n = 5.38428 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (428) and 2 digits in the non-repeating part (38). Multiply both sides by 10⁵ = 100000.

100000 × n = 538428.428 (equation 2)

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

100000 × n = 538428.428
   100 × n = 5.38428
 99900 × n = 537890

53789099900 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 = 53789099900 = 537890 ÷ 1099900 ÷ 10 = 537899990. So,

5.38428 = 537899990 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 537899990 is also equal to 538399990 when expressed as a mixed number.

The repeating decimal 5.38428 (vinculum notation) has a repeated block length of 3. It is also represented as 5.38428428428... (ellipsis notation) which equals approximately 5.38428428428428428 (decimal approximation)(*).

The recurring decimal 5.38428 can be written as a ratio of two integers having 53789 as the numerator and 9990 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.