What is 2.9461461461... as a Fraction?

2.9461 equals 147164995 as a fraction.

How do you turn 2.9461 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.9461 repeating into a fraction, begin writing this simple equation:

n = 2.9461 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (461) and 1 digit in the non-repeating part (9). Multiply both sides by 10⁴ = 10000.

10000 × n = 29461.461 (equation 2)

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

10000 × n = 29461.461
   10 × n = 2.9461
 9990 × n = 29432

294329990 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 = 294329990 = 29432 ÷ 29990 ÷ 2 = 147164995. So,

2.9461 = 147164995 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 147164995 is also equal to 247264995 when expressed as a mixed number.

The repeating decimal 2.9461 (vinculum notation) has a repeated block length of 3. It is also represented as 2.9461461461... (ellipsis notation) which equals approximately 2.9461461461461461 (decimal approximation)(*).

The recurring decimal 2.9461 can be written as a ratio of two integers having 14716 as the numerator and 4995 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.