What is 172.8777... as a Fraction?

172.87 equals 1555990 as a fraction.

How do you turn 172.87 repeating into a fraction?

Detailed Answer:

Step 1: To convert 172.87 repeating into a fraction, begin writing this simple equation:

n = 172.87 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7) and 1 digit in the non-repeating part (8). Multiply both sides by 10² = 100.

100 × n = 17287.7 (equation 2)

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

100 × n = 17287.7
 10 × n = 172.87
 90 × n = 15559

n = 1555990 (answer)

172.87 = 1555990 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 1555990 is also equal to 1727990 when expressed as a mixed number.

The repeating decimal 172.87 (vinculum notation) has a repeated block length of 1. It is also represented as 172.8777... (ellipsis notation) which equals approximately 172.877777 (decimal approximation)(*).

The recurring decimal 172.87 can be written as a ratio of two integers having 15559 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.