What is 100.13333... as a Fraction?

100.133 equals 150215 as a fraction.

How do you turn 100.133 repeating into a fraction?

Detailed Answer:

Step 1: To convert 100.133 repeating into a fraction, begin writing this simple equation:

n = 100.133 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 100133.3 (equation 2)

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

1000 × n = 100133.3
 100 × n = 100.133
 900 × n = 90120

90120900 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 = 90120900 = 90120 ÷ 60900 ÷ 60 = 150215. So,

100.133 = 150215 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 150215 is also equal to 100215 when expressed as a mixed number.

The repeating decimal 100.133 (vinculum notation) has a repeated block length of 1. It is also represented as 100.13333... (ellipsis notation) which equals approximately 100.1333333 (decimal approximation)(*).

The recurring decimal 100.133 can be written as a ratio of two integers having 1502 as the numerator and 15 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.