What is 0.17153153153... as a Fraction?

0.17153 equals 4762775 as a fraction.

How do you turn 0.17153 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.17153 repeating into a fraction, begin writing this simple equation:

n = 0.17153 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (153) and 2 digits in the non-repeating part (17). Multiply both sides by 10⁵ = 100000.

100000 × n = 17153.153 (equation 2)

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

100000 × n = 17153.153
   100 × n = 0.17153
 99900 × n = 17136

1713699900 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 36 (the GCF - greatest common factor).

n = 1713699900 = 17136 ÷ 3699900 ÷ 36 = 4762775. So,

0.17153 = 4762775 as the lowest possible fraction.

The repeating decimal 0.17153 (vinculum notation) has a repeated block length of 3. It is also represented as 0.17153153153... (ellipsis notation) which equals approximately 0.17153153153153153 (decimal approximation)(*).

The recurring decimal 0.17153 can be written as a ratio of two integers having 476 as the numerator and 2775 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.