What is 0.1772727272... as a Fraction?

0.1772 equals 39220 as a fraction.

How do you turn 0.1772 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1772 repeating into a fraction, begin writing this simple equation:

n = 0.1772 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (72) and 2 digits in the non-repeating part (17). Multiply both sides by 10⁴ = 10000.

10000 × n = 1772.72 (equation 2)

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

10000 × n = 1772.72
  100 × n = 0.1772
 9900 × n = 1755

17559900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 45 (the GCF - greatest common factor).

n = 17559900 = 1755 ÷ 459900 ÷ 45 = 39220. So,

0.1772 = 39220 as the lowest possible fraction.

The repeating decimal 0.1772 (vinculum notation) has a repeated block length of 2. It is also represented as 0.17727272... (ellipsis notation) which equals approximately 0.177272727272 (decimal approximation)(*).

The recurring decimal 0.1772 can be written as a ratio of two integers having 39 as the numerator and 220 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.