What is 47.10444... as a Fraction?

47.104 equals 21197450 as a fraction.

How do you turn 47.104 repeating into a fraction?

Detailed Answer:

Step 1: To convert 47.104 repeating into a fraction, begin writing this simple equation:

n = 47.104 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (4) and 2 digits in the non-repeating part (10). Multiply both sides by 10³ = 1000.

1000 × n = 47104.4 (equation 2)

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

1000 × n = 47104.4
 100 × n = 47.104
 900 × n = 42394

42394900 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 2 (the GCF - greatest common factor).

n = 42394900 = 42394 ÷ 2900 ÷ 2 = 21197450. So,

47.104 = 21197450 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 21197450 is also equal to 4747450 when expressed as a mixed number.

The repeating decimal 47.104 (vinculum notation) has a repeated block length of 1. It is also represented as 47.10444... (ellipsis notation) which equals approximately 47.1044444 (decimal approximation)(*).

The recurring decimal 47.104 can be written as a ratio of two integers having 21197 as the numerator and 450 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.