What is 348.133... as a Fraction?

348.133 equals 522215 as a fraction.

How do you turn 348.133 repeating into a fraction?

Detailed Answer:

Step 1: To convert 348.133 repeating into a fraction, begin writing this simple equation:

n = 348.133 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 348133.3 (equation 2)

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

1000 × n = 348133.3
 100 × n = 348.133
 900 × n = 313320

313320900 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 60 (the GCF - greatest common factor).

n = 313320900 = 313320 ÷ 60900 ÷ 60 = 522215. So,

348.133 = 522215 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 522215 is also equal to 348215 when expressed as a mixed number.

The repeating decimal 348.133 (vinculum notation) has a repeated block length of 1. It is also represented as 348.13333... (ellipsis notation) which equals approximately 348.1333333 (decimal approximation)(*).

The recurring decimal 348.133 can be written as a ratio of two integers having 5222 as the numerator and 15 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.