What is 0.10428428428... as a Fraction?

0.10428 equals 520949950 as a fraction.

How do you turn 0.10428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.10428 repeating into a fraction, begin writing this simple equation:

n = 0.10428 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (428) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁵ = 100000.

100000 × n = 10428.428 (equation 2)

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

100000 × n = 10428.428
   100 × n = 0.10428
 99900 × n = 10418

1041899900 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 2 (the GCF - greatest common factor).

n = 1041899900 = 10418 ÷ 299900 ÷ 2 = 520949950. So,

0.10428 = 520949950 as the lowest possible fraction.

The repeating decimal 0.10428 (vinculum notation) has a repeated block length of 3. It is also represented as 0.10428428428... (ellipsis notation) which equals approximately 0.10428428428428428 (decimal approximation)(*).

The recurring decimal 0.10428 can be written as a ratio of two integers having 5209 as the numerator and 49950 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.