What is 3.7428428428... as a Fraction?

3.7428 equals 373919990 as a fraction.

How do you turn 3.7428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 3.7428 repeating into a fraction, begin writing this simple equation:

n = 3.7428 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (428) and 1 digit in the non-repeating part (7). Multiply both sides by 10⁴ = 10000.

10000 × n = 37428.428 (equation 2)

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

10000 × n = 37428.428
   10 × n = 3.7428
 9990 × n = 37391

n = 373919990 (answer)

3.7428 = 373919990 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 373919990 is also equal to 374219990 when expressed as a mixed number.

The repeating decimal 3.7428 (vinculum notation) has a repeated block length of 3. It is also represented as 3.7428428428... (ellipsis notation) which equals approximately 3.7428428428428428 (decimal approximation)(*).

The recurring decimal 3.7428 can be written as a ratio of two integers having 37391 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.