What is 1.14714714714... as a Fraction?

1.14714 equals 382333 as a fraction.

How do you turn 1.14714 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.14714 repeating into a fraction, begin writing this simple equation:

n = 1.14714 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (714) and 2 digits in the non-repeating part (14). Multiply both sides by 10⁵ = 100000.

100000 × n = 114714.714 (equation 2)

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

100000 × n = 114714.714
   100 × n = 1.14714
 99900 × n = 114600

11460099900 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 300 (the GCF - greatest common factor).

n = 11460099900 = 114600 ÷ 30099900 ÷ 300 = 382333. So,

1.14714 = 382333 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 382333 is also equal to 149333 when expressed as a mixed number.

The repeating decimal 1.14714 (vinculum notation) has a repeated block length of 3. It is also represented as 1.14714714714... (ellipsis notation) which equals approximately 1.14714714714714714 (decimal approximation)(*).

The recurring decimal 1.14714 can be written as a ratio of two integers having 382 as the numerator and 333 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.