What is 4.37307307307... as a Fraction?

4.37307 equals 436879990 as a fraction.

How do you turn 4.37307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.37307 repeating into a fraction, begin writing this simple equation:

n = 4.37307 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (307) and 2 digits in the non-repeating part (37). Multiply both sides by 10⁵ = 100000.

100000 × n = 437307.307 (equation 2)

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

100000 × n = 437307.307
   100 × n = 4.37307
 99900 × n = 436870

43687099900 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 = 43687099900 = 436870 ÷ 1099900 ÷ 10 = 436879990. So,

4.37307 = 436879990 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 436879990 is also equal to 437279990 when expressed as a mixed number.

The repeating decimal 4.37307 (vinculum notation) has a repeated block length of 3. It is also represented as 4.37307307307... (ellipsis notation) which equals approximately 4.37307307307307307 (decimal approximation)(*).

The recurring decimal 4.37307 can be written as a ratio of two integers having 43687 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.