What is 36.14555... as a Fraction?

36.145 equals 32531900 as a fraction.

How do you turn 36.145 repeating into a fraction?

Detailed Answer:

Step 1: To convert 36.145 repeating into a fraction, begin writing this simple equation:

n = 36.145 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5) and 2 digits in the non-repeating part (14). Multiply both sides by 10³ = 1000.

1000 × n = 36145.5 (equation 2)

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

1000 × n = 36145.5
 100 × n = 36.145
 900 × n = 32531

n = 32531900 (answer)

36.145 = 32531900 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 32531900 is also equal to 36131900 when expressed as a mixed number.

The repeating decimal 36.145 (vinculum notation) has a repeated block length of 1. It is also represented as 36.14555... (ellipsis notation) which equals approximately 36.1455555 (decimal approximation)(*).

The recurring decimal 36.145 can be written as a ratio of two integers having 32531 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.