What is 1.2802020202... as a Fraction?

1.2802 equals 63374950 as a fraction.

How do you turn 1.2802 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.2802 repeating into a fraction, begin writing this simple equation:

n = 1.2802 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (02) and 2 digits in the non-repeating part (28). Multiply both sides by 10⁴ = 10000.

10000 × n = 12802.02 (equation 2)

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

10000 × n = 12802.02
  100 × n = 1.2802
 9900 × n = 12674

126749900 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 = 126749900 = 12674 ÷ 29900 ÷ 2 = 63374950. So,

1.2802 = 63374950 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 63374950 is also equal to 113874950 when expressed as a mixed number.

The repeating decimal 1.2802 (vinculum notation) has a repeated block length of 2. It is also represented as 1.28020202... (ellipsis notation) which equals approximately 1.280202020202 (decimal approximation)(*).

The recurring decimal 1.2802 can be written as a ratio of two integers having 6337 as the numerator and 4950 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.