What is 48.173... as a Fraction?

48.173 equals 361375 as a fraction.

How do you turn 48.173 repeating into a fraction?

Detailed Answer:

Step 1: To convert 48.173 repeating into a fraction, begin writing this simple equation:

n = 48.173 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (17). Multiply both sides by 10³ = 1000.

1000 × n = 48173.3 (equation 2)

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

1000 × n = 48173.3
 100 × n = 48.173
 900 × n = 43356

43356900 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 12 (the GCF - greatest common factor).

n = 43356900 = 43356 ÷ 12900 ÷ 12 = 361375. So,

48.173 = 361375 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 361375 is also equal to 481375 when expressed as a mixed number.

The repeating decimal 48.173 (vinculum notation) has a repeated block length of 1. It is also represented as 48.17333... (ellipsis notation) which equals approximately 48.1733333 (decimal approximation)(*).

The recurring decimal 48.173 can be written as a ratio of two integers having 3613 as the numerator and 75 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.