What is 5.250303... as a Fraction?

5.2503 equals 86631650 as a fraction.

How do you turn 5.2503 repeating into a fraction?

Detailed Answer:

Step 1: To convert 5.2503 repeating into a fraction, begin writing this simple equation:

n = 5.2503 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (03) and 2 digits in the non-repeating part (25). Multiply both sides by 10⁴ = 10000.

10000 × n = 52503.03 (equation 2)

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

10000 × n = 52503.03
  100 × n = 5.2503
 9900 × n = 51978

519789900 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 6 (the GCF - greatest common factor).

n = 519789900 = 51978 ÷ 69900 ÷ 6 = 86631650. So,

5.2503 = 86631650 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 86631650 is also equal to 54131650 when expressed as a mixed number.

The repeating decimal 5.2503 (vinculum notation) has a repeated block length of 2. It is also represented as 5.25030303... (ellipsis notation) which equals approximately 5.250303030303 (decimal approximation)(*).

The recurring decimal 5.2503 can be written as a ratio of two integers having 8663 as the numerator and 1650 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.