What is 16.182323... as a Fraction?

16.1823 equals 320411980 as a fraction.

How do you turn 16.1823 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.1823 repeating into a fraction, begin writing this simple equation:

n = 16.1823 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (23) and 2 digits in the non-repeating part (18). Multiply both sides by 10⁴ = 10000.

10000 × n = 161823.23 (equation 2)

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

10000 × n = 161823.23
  100 × n = 16.1823
 9900 × n = 160205

1602059900 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 5 (the GCF - greatest common factor).

n = 1602059900 = 160205 ÷ 59900 ÷ 5 = 320411980. So,

16.1823 = 320411980 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 320411980 is also equal to 163611980 when expressed as a mixed number.

The repeating decimal 16.1823 (vinculum notation) has a repeated block length of 2. It is also represented as 16.18232323... (ellipsis notation) which equals approximately 16.182323232323 (decimal approximation)(*).

The recurring decimal 16.1823 can be written as a ratio of two integers having 32041 as the numerator and 1980 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.