What is 4.272307230723072307... as a Fraction?

4.272307 equals 7119816665 as a fraction.

How do you turn 4.272307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.272307 repeating into a fraction, begin writing this simple equation:

n = 4.272307 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (2307) and 2 digits in the non-repeating part (27). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 4272307.2307 (equation 2)

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

1000000 × n = 4272307.2307
    100 × n = 4.272307
 999900 × n = 4271880

4271880999900 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 60 (the GCF - greatest common factor).

n = 4271880999900 = 4271880 ÷ 60999900 ÷ 60 = 7119816665. So,

4.272307 = 7119816665 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 7119816665 is also equal to 4453816665 when expressed as a mixed number.

The repeating decimal 4.272307 (vinculum notation) has a repeated block length of 4. It is also represented as 4.27230723072307... (ellipsis notation) which equals approximately 4.2723072307230723072307 (decimal approximation)(*).

The recurring decimal 4.272307 can be written as a ratio of two integers having 71198 as the numerator and 16665 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.