What is 6.5292929... as a Fraction?

6.529 equals 3232495 as a fraction.

How do you turn 6.529 repeating into a fraction?

Detailed Answer:

Step 1: To convert 6.529 repeating into a fraction, begin writing this simple equation:

n = 6.529 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (29) and 1 digit in the non-repeating part (5). Multiply both sides by 10³ = 1000.

1000 × n = 6529.29 (equation 2)

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

1000 × n = 6529.29
  10 × n = 6.529
 990 × n = 6464

6464990 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 = 6464990 = 6464 ÷ 2990 ÷ 2 = 3232495. So,

6.529 = 3232495 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 3232495 is also equal to 6262495 when expressed as a mixed number.

The repeating decimal 6.529 (vinculum notation) has a repeated block length of 2. It is also represented as 6.5292929... (ellipsis notation) which equals approximately 6.52929292929 (decimal approximation)(*).

The recurring decimal 6.529 can be written as a ratio of two integers having 3232 as the numerator and 495 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.