What is 0.17272... as a Fraction?

0.172 equals 19110 as a fraction.

How do you turn 0.172 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.172 repeating into a fraction, begin writing this simple equation:

n = 0.172 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (72) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 172.72 (equation 2)

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

1000 × n = 172.72
  10 × n = 0.172
 990 × n = 171

171990 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 9 (the GCF - greatest common factor).

n = 171990 = 171 ÷ 9990 ÷ 9 = 19110. So,

0.172 = 19110 as the lowest possible fraction.

The repeating decimal 0.172 (vinculum notation) has a repeated block length of 2. It is also represented as 0.1727272... (ellipsis notation) which equals approximately 0.17272727272 (decimal approximation)(*).

The recurring decimal 0.172 can be written as a ratio of two integers having 19 as the numerator and 110 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.