What is 0.41333... as a Fraction?

0.413 equals 3175 as a fraction.

How do you turn 0.413 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.413 repeating into a fraction, begin writing this simple equation:

n = 0.413 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (41). Multiply both sides by 10³ = 1000.

1000 × n = 413.3 (equation 2)

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

1000 × n = 413.3
 100 × n = 0.413
 900 × n = 372

372900 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 = 372900 = 372 ÷ 12900 ÷ 12 = 3175. So,

0.413 = 3175 as the lowest possible fraction.

The repeating decimal 0.413 (vinculum notation) has a repeated block length of 1. It is also represented as 0.41333... (ellipsis notation) which equals approximately 0.4133333 (decimal approximation)(*).

The recurring decimal 0.413 can be written as a ratio of two integers having 31 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.