What is 14.00303... as a Fraction?

14.03 equals 4621330 as a fraction.

How do you turn 14.03 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.03 repeating into a fraction, begin writing this simple equation:

n = 14.03 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (03), so multiply both sides by 10² = 100.

100 × n = 1403.03 (equation 2)

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

100 × n = 1403.03
  1 × n = 14.03
 99 × n = 1389

138999 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 = 138999 = 1389 ÷ 399 ÷ 3 = 4621330. So,

14.03 = 4621330 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 4621330 is also equal to 141330 when expressed as a mixed number.

The repeating decimal 14.03 (vinculum notation) has a repeated block length of 2. It is also represented as 14.030303... (ellipsis notation) which equals approximately 14.0303030303 (decimal approximation)(*).

The recurring decimal 14.03 can be written as a ratio of two integers having 4621 as the numerator and 330 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.