What is 100.21111... as a Fraction?

100.211 equals 901990 as a fraction.

How do you turn 100.211 repeating into a fraction?

Detailed Answer:

Step 1: To convert 100.211 repeating into a fraction, begin writing this simple equation:

n = 100.211 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (1) and 2 digits in the non-repeating part (21). Multiply both sides by 10³ = 1000.

1000 × n = 100211.1 (equation 2)

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

1000 × n = 100211.1
 100 × n = 100.211
 900 × n = 90190

90190900 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 = 90190900 = 90190 ÷ 10900 ÷ 10 = 901990. So,

100.211 = 901990 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 901990 is also equal to 1001990 when expressed as a mixed number.

The repeating decimal 100.211 (vinculum notation) has a repeated block length of 1. It is also represented as 100.21111... (ellipsis notation) which equals approximately 100.2111111 (decimal approximation)(*).

The recurring decimal 100.211 can be written as a ratio of two integers having 9019 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.