What is 46.444... as a Fraction?

46.4 equals 4189 as a fraction.

How do you turn 46.4 repeating into a fraction?

Detailed Answer:

Step 1: To convert 46.4 repeating into a fraction, begin writing this simple equation:

n = 46.4 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (4), so multiply both sides by 10¹ = 10.

10 × n = 464.4 (equation 2)

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

10 × n = 464.4
 1 × n = 46.4
 9 × n = 418

n = 4189 (answer)

46.4 = 4189 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 4189 is also equal to 4649 when expressed as a mixed number.

The repeating decimal 46.4 (vinculum notation) has a repeated block length of 1. It is also represented as 46.444... (ellipsis notation) which equals approximately 46.44444 (decimal approximation)(*).

The recurring decimal 46.4 can be written as a ratio of two integers having 418 as the numerator and 9 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.