What is 5.69444... as a Fraction?

5.694 equals 20536 as a fraction.

How do you turn 5.694 repeating into a fraction?

Detailed Answer:

Step 1: To convert 5.694 repeating into a fraction, begin writing this simple equation:

n = 5.694 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (4) and 2 digits in the non-repeating part (69). Multiply both sides by 10³ = 1000.

1000 × n = 5694.4 (equation 2)

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

1000 × n = 5694.4
 100 × n = 5.694
 900 × n = 5125

5125900 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 25 (the GCF - greatest common factor).

n = 5125900 = 5125 ÷ 25900 ÷ 25 = 20536. So,

5.694 = 20536 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 20536 is also equal to 52536 when expressed as a mixed number.

The repeating decimal 5.694 (vinculum notation) has a repeated block length of 1. It is also represented as 5.69444... (ellipsis notation) which equals approximately 5.6944444 (decimal approximation)(*).

The recurring decimal 5.694 can be written as a ratio of two integers having 205 as the numerator and 36 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.