What is 172.0777... as a Fraction?

172.7 equals 1548790 as a fraction.

How do you turn 172.7 repeating into a fraction?

Detailed Answer:

Step 1: To convert 172.7 repeating into a fraction, begin writing this simple equation:

n = 172.7 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7), so multiply both sides by 10¹ = 10.

10 × n = 1727.7 (equation 2)

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

10 × n = 1727.7
 1 × n = 172.7
 9 × n = 1555

n = 1548790 (answer)

172.7 = 1548790 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 1548790 is also equal to 172790 when expressed as a mixed number.

The repeating decimal 172.7 (vinculum notation) has a repeated block length of 1. It is also represented as 172.777... (ellipsis notation) which equals approximately 172.77777 (decimal approximation)(*).

The recurring decimal 172.7 can be written as a ratio of two integers having 15487 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.