What is 100.6111... as a Fraction?

100.61 equals 181118 as a fraction.

How do you turn 100.61 repeating into a fraction?

Detailed Answer:

Step 1: To convert 100.61 repeating into a fraction, begin writing this simple equation:

n = 100.61 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (1) and 1 digit in the non-repeating part (6). Multiply both sides by 10² = 100.

100 × n = 10061.1 (equation 2)

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

100 × n = 10061.1
 10 × n = 100.61
 90 × n = 9055

905590 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 5 (the GCF - greatest common factor).

n = 905590 = 9055 ÷ 590 ÷ 5 = 181118. So,

100.61 = 181118 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 181118 is also equal to 1001118 when expressed as a mixed number.

The repeating decimal 100.61 (vinculum notation) has a repeated block length of 1. It is also represented as 100.6111... (ellipsis notation) which equals approximately 100.611111 (decimal approximation)(*).

The recurring decimal 100.61 can be written as a ratio of two integers having 1811 as the numerator and 18 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.