What is 0.479090... as a Fraction?

0.4790 equals 5271100 as a fraction.

How do you turn 0.4790 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.4790 repeating into a fraction, begin writing this simple equation:

n = 0.4790 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (90) and 2 digits in the non-repeating part (47). Multiply both sides by 10⁴ = 10000.

10000 × n = 4790.90 (equation 2)

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

10000 × n = 4790.90
  100 × n = 0.4790
 9900 × n = 4743

47439900 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 9 (the GCF - greatest common factor).

n = 47439900 = 4743 ÷ 99900 ÷ 9 = 5271100. So,

0.4790 = 5271100 as the lowest possible fraction.

The repeating decimal 0.4790 (vinculum notation) has a repeated block length of 2. It is also represented as 0.47909090... (ellipsis notation) which equals approximately 0.479090909090 (decimal approximation)(*).

The recurring decimal 0.4790 can be written as a ratio of two integers having 527 as the numerator and 1100 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.