What is 1.147142871428714287142871428... as a Fraction?

1.1471428 equals 57356574999950 as a fraction.

How do you turn 1.1471428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.1471428 repeating into a fraction, begin writing this simple equation:

n = 1.1471428 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (71428) and 2 digits in the non-repeating part (14). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 11471428.71428 (equation 2)

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

10000000 × n = 11471428.71428
     100 × n = 1.1471428
 9999900 × n = 11471314

114713149999900 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 = 114713149999900 = 11471314 ÷ 29999900 ÷ 2 = 57356574999950. So,

1.1471428 = 57356574999950 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 57356574999950 is also equal to 17357074999950 when expressed as a mixed number.

The repeating decimal 1.1471428 (vinculum notation) has a repeated block length of 5. It is also represented as 1.14714287142871428... (ellipsis notation) which equals approximately 1.147142871428714287142871428 (decimal approximation)(*).

The recurring decimal 1.1471428 can be written as a ratio of two integers having 5735657 as the numerator and 4999950 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.