What is 171.8777... as a Fraction?

171.87 equals 1546990 as a fraction.

How do you turn 171.87 repeating into a fraction?

Detailed Answer:

Step 1: To convert 171.87 repeating into a fraction, begin writing this simple equation:

n = 171.87 (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 = 17187.7 (equation 2)

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

100 × n = 17187.7
 10 × n = 171.87
 90 × n = 15469

n = 1546990 (answer)

171.87 = 1546990 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 1546990 is also equal to 1717990 when expressed as a mixed number.

The repeating decimal 171.87 (vinculum notation) has a repeated block length of 1. It is also represented as 171.8777... (ellipsis notation) which equals approximately 171.877777 (decimal approximation)(*).

The recurring decimal 171.87 can be written as a ratio of two integers having 15469 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.