What is 7.272857285728572857... as a Fraction?

7.272857 equals 72721399990 as a fraction.

How do you turn 7.272857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 7.272857 repeating into a fraction, begin writing this simple equation:

n = 7.272857 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (2857) and 2 digits in the non-repeating part (27). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 7272857.2857 (equation 2)

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

1000000 × n = 7272857.2857
    100 × n = 7.272857
 999900 × n = 7272130

7272130999900 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 = 7272130999900 = 7272130 ÷ 10999900 ÷ 10 = 72721399990. So,

7.272857 = 72721399990 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 72721399990 is also equal to 72728399990 when expressed as a mixed number.

The repeating decimal 7.272857 (vinculum notation) has a repeated block length of 4. It is also represented as 7.27285728572857... (ellipsis notation) which equals approximately 7.2728572857285728572857 (decimal approximation)(*).

The recurring decimal 7.272857 can be written as a ratio of two integers having 727213 as the numerator and 99990 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.