What is 0.16428428428... as a Fraction?

0.16428 equals 410324975 as a fraction.

How do you turn 0.16428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.16428 repeating into a fraction, begin writing this simple equation:

n = 0.16428 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (428) and 2 digits in the non-repeating part (16). Multiply both sides by 10⁵ = 100000.

100000 × n = 16428.428 (equation 2)

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

100000 × n = 16428.428
   100 × n = 0.16428
 99900 × n = 16412

1641299900 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 4 (the GCF - greatest common factor).

n = 1641299900 = 16412 ÷ 499900 ÷ 4 = 410324975. So,

0.16428 = 410324975 as the lowest possible fraction.

The repeating decimal 0.16428 (vinculum notation) has a repeated block length of 3. It is also represented as 0.16428428428... (ellipsis notation) which equals approximately 0.16428428428428428 (decimal approximation)(*).

The recurring decimal 0.16428 can be written as a ratio of two integers having 4103 as the numerator and 24975 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.