What is 172.10777... as a Fraction?

172.107 equals 154897900 as a fraction.

How do you turn 172.107 repeating into a fraction?

Detailed Answer:

Step 1: To convert 172.107 repeating into a fraction, begin writing this simple equation:

n = 172.107 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7) and 2 digits in the non-repeating part (10). Multiply both sides by 10³ = 1000.

1000 × n = 172107.7 (equation 2)

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

1000 × n = 172107.7
 100 × n = 172.107
 900 × n = 154897

n = 154897900 (answer)

172.107 = 154897900 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 154897900 is also equal to 17297900 when expressed as a mixed number.

The repeating decimal 172.107 (vinculum notation) has a repeated block length of 1. It is also represented as 172.10777... (ellipsis notation) which equals approximately 172.1077777 (decimal approximation)(*).

The recurring decimal 172.107 can be written as a ratio of two integers having 154897 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.