What is 72.18888... as a Fraction?

72.188 equals 649790 as a fraction.

How do you turn 72.188 repeating into a fraction?

Detailed Answer:

Step 1: To convert 72.188 repeating into a fraction, begin writing this simple equation:

n = 72.188 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (18). Multiply both sides by 10³ = 1000.

1000 × n = 72188.8 (equation 2)

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

1000 × n = 72188.8
 100 × n = 72.188
 900 × n = 64970

64970900 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 = 64970900 = 64970 ÷ 10900 ÷ 10 = 649790. So,

72.188 = 649790 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 649790 is also equal to 721790 when expressed as a mixed number.

The repeating decimal 72.188 (vinculum notation) has a repeated block length of 1. It is also represented as 72.18888... (ellipsis notation) which equals approximately 72.1888888 (decimal approximation)(*).

The recurring decimal 72.188 can be written as a ratio of two integers having 6497 as the numerator and 90 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.