What is 19.555... as a Fraction?

19.5 equals 1769 as a fraction.

How do you turn 19.5 repeating into a fraction?

Detailed Answer:

Step 1: To convert 19.5 repeating into a fraction, begin writing this simple equation:

n = 19.5 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5), so multiply both sides by 10¹ = 10.

10 × n = 195.5 (equation 2)

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

10 × n = 195.5
 1 × n = 19.5
 9 × n = 176

n = 1769 (answer)

19.5 = 1769 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 1769 is also equal to 1959 when expressed as a mixed number.

The repeating decimal 19.5 (vinculum notation) has a repeated block length of 1. It is also represented as 19.555... (ellipsis notation) which equals approximately 19.55555 (decimal approximation)(*).

The recurring decimal 19.5 can be written as a ratio of two integers having 176 as the numerator and 9 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.