What is 37.12555... as a Fraction?

37.125 equals 33413900 as a fraction.

How do you turn 37.125 repeating into a fraction?

Detailed Answer:

Step 1: To convert 37.125 repeating into a fraction, begin writing this simple equation:

n = 37.125 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5) and 2 digits in the non-repeating part (12). Multiply both sides by 10³ = 1000.

1000 × n = 37125.5 (equation 2)

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

1000 × n = 37125.5
 100 × n = 37.125
 900 × n = 33413

n = 33413900 (answer)

37.125 = 33413900 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 33413900 is also equal to 37113900 when expressed as a mixed number.

The repeating decimal 37.125 (vinculum notation) has a repeated block length of 1. It is also represented as 37.12555... (ellipsis notation) which equals approximately 37.1255555 (decimal approximation)(*).

The recurring decimal 37.125 can be written as a ratio of two integers having 33413 as the numerator and 900 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.