What is 0.100222... as a Fraction?

0.1002 equals 4514500 as a fraction.

How do you turn 0.1002 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1002 repeating into a fraction, begin writing this simple equation:

n = 0.1002 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 3 digits in the non-repeating part (100). Multiply both sides by 10⁴ = 10000.

10000 × n = 1002.2 (equation 2)

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

10000 × n = 1002.2
 1000 × n = 0.1002
 9000 × n = 902

9029000 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 = 9029000 = 902 ÷ 29000 ÷ 2 = 4514500. So,

0.1002 = 4514500 as the lowest possible fraction.

The repeating decimal 0.1002 (vinculum notation) has a repeated block length of 1. It is also represented as 0.100222... (ellipsis notation) which equals approximately 0.10022222 (decimal approximation)(*).

The recurring decimal 0.1002 can be written as a ratio of two integers having 451 as the numerator and 4500 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.