What is 4.30101... as a Fraction?

4.301 equals 2129495 as a fraction.

How do you turn 4.301 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.301 repeating into a fraction, begin writing this simple equation:

n = 4.301 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (01) and 1 digit in the non-repeating part (3). Multiply both sides by 10³ = 1000.

1000 × n = 4301.01 (equation 2)

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

1000 × n = 4301.01
  10 × n = 4.301
 990 × n = 4258

4258990 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 = 4258990 = 4258 ÷ 2990 ÷ 2 = 2129495. So,

4.301 = 2129495 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 2129495 is also equal to 4149495 when expressed as a mixed number.

The repeating decimal 4.301 (vinculum notation) has a repeated block length of 2. It is also represented as 4.3010101... (ellipsis notation) which equals approximately 4.30101010101 (decimal approximation)(*).

The recurring decimal 4.301 can be written as a ratio of two integers having 2129 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.