What is 7.37384384384... as a Fraction?

7.37384 equals 24554933300 as a fraction.

How do you turn 7.37384 repeating into a fraction?

Detailed Answer:

Step 1: To convert 7.37384 repeating into a fraction, begin writing this simple equation:

n = 7.37384 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (384) and 2 digits in the non-repeating part (37). Multiply both sides by 10⁵ = 100000.

100000 × n = 737384.384 (equation 2)

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

100000 × n = 737384.384
   100 × n = 7.37384
 99900 × n = 736647

73664799900 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 3 (the GCF - greatest common factor).

n = 73664799900 = 736647 ÷ 399900 ÷ 3 = 24554933300. So,

7.37384 = 24554933300 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 24554933300 is also equal to 71244933300 when expressed as a mixed number.

The repeating decimal 7.37384 (vinculum notation) has a repeated block length of 3. It is also represented as 7.37384384384... (ellipsis notation) which equals approximately 7.37384384384384384 (decimal approximation)(*).

The recurring decimal 7.37384 can be written as a ratio of two integers having 245549 as the numerator and 33300 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.