What is 47.233333... as a Fraction?

47.233 equals 141730 as a fraction.

How do you turn 47.233 repeating into a fraction?

Detailed Answer:

Step 1: To convert 47.233 repeating into a fraction, begin writing this simple equation:

n = 47.233 (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 = 47233.3 (equation 2)

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

1000 × n = 47233.3
 100 × n = 47.233
 900 × n = 42510

42510900 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 = 42510900 = 42510 ÷ 30900 ÷ 30 = 141730. So,

47.233 = 141730 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 141730 is also equal to 47730 when expressed as a mixed number.

The repeating decimal 47.233 (vinculum notation) has a repeated block length of 1. It is also represented as 47.23333... (ellipsis notation) which equals approximately 47.2333333 (decimal approximation)(*).

The recurring decimal 47.233 can be written as a ratio of two integers having 1417 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.