What is 18.70222... as a Fraction?

18.702 equals 4208225 as a fraction.

How do you turn 18.702 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.702 repeating into a fraction, begin writing this simple equation:

n = 18.702 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 2 digits in the non-repeating part (70). Multiply both sides by 10³ = 1000.

1000 × n = 18702.2 (equation 2)

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

1000 × n = 18702.2
 100 × n = 18.702
 900 × n = 16832

16832900 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 = 16832900 = 16832 ÷ 4900 ÷ 4 = 4208225. So,

18.702 = 4208225 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 4208225 is also equal to 18158225 when expressed as a mixed number.

The repeating decimal 18.702 (vinculum notation) has a repeated block length of 1. It is also represented as 18.70222... (ellipsis notation) which equals approximately 18.7022222 (decimal approximation)(*).

The recurring decimal 18.702 can be written as a ratio of two integers having 4208 as the numerator and 225 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.