What is 330.1633... as a Fraction?

330.163 equals 99049300 as a fraction.

How do you turn 330.163 repeating into a fraction?

Detailed Answer:

Step 1: To convert 330.163 repeating into a fraction, begin writing this simple equation:

n = 330.163 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (16). Multiply both sides by 10³ = 1000.

1000 × n = 330163.3 (equation 2)

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

1000 × n = 330163.3
 100 × n = 330.163
 900 × n = 297147

297147900 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 3 (the GCF - greatest common factor).

n = 297147900 = 297147 ÷ 3900 ÷ 3 = 99049300. So,

330.163 = 99049300 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 99049300 is also equal to 33049300 when expressed as a mixed number.

The repeating decimal 330.163 (vinculum notation) has a repeated block length of 1. It is also represented as 330.16333... (ellipsis notation) which equals approximately 330.1633333 (decimal approximation)(*).

The recurring decimal 330.163 can be written as a ratio of two integers having 99049 as the numerator and 300 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.