What is 329.183... as a Fraction?

329.183 equals 1975160 as a fraction.

How do you turn 329.183 repeating into a fraction?

Detailed Answer:

Step 1: To convert 329.183 repeating into a fraction, begin writing this simple equation:

n = 329.183 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (18). Multiply both sides by 10³ = 1000.

1000 × n = 329183.3 (equation 2)

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

1000 × n = 329183.3
 100 × n = 329.183
 900 × n = 296265

296265900 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 15 (the GCF - greatest common factor).

n = 296265900 = 296265 ÷ 15900 ÷ 15 = 1975160. So,

329.183 = 1975160 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 1975160 is also equal to 3291160 when expressed as a mixed number.

The repeating decimal 329.183 (vinculum notation) has a repeated block length of 1. It is also represented as 329.18333... (ellipsis notation) which equals approximately 329.1833333 (decimal approximation)(*).

The recurring decimal 329.183 can be written as a ratio of two integers having 19751 as the numerator and 60 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.