What is 46.233333... as a Fraction?

46.233 equals 138730 as a fraction.

How do you turn 46.233 repeating into a fraction?

Detailed Answer:

Step 1: To convert 46.233 repeating into a fraction, begin writing this simple equation:

n = 46.233 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (23). Multiply both sides by 10³ = 1000.

1000 × n = 46233.3 (equation 2)

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

1000 × n = 46233.3
 100 × n = 46.233
 900 × n = 41610

41610900 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 30 (the GCF - greatest common factor).

n = 41610900 = 41610 ÷ 30900 ÷ 30 = 138730. So,

46.233 = 138730 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 138730 is also equal to 46730 when expressed as a mixed number.

The repeating decimal 46.233 (vinculum notation) has a repeated block length of 1. It is also represented as 46.23333... (ellipsis notation) which equals approximately 46.2333333 (decimal approximation)(*).

The recurring decimal 46.233 can be written as a ratio of two integers having 1387 as the numerator and 30 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.