What is 80.25333... as a Fraction?

80.253 equals 601975 as a fraction.

How do you turn 80.253 repeating into a fraction?

Detailed Answer:

Step 1: To convert 80.253 repeating into a fraction, begin writing this simple equation:

n = 80.253 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (25). Multiply both sides by 10³ = 1000.

1000 × n = 80253.3 (equation 2)

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

1000 × n = 80253.3
 100 × n = 80.253
 900 × n = 72228

72228900 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 12 (the GCF - greatest common factor).

n = 72228900 = 72228 ÷ 12900 ÷ 12 = 601975. So,

80.253 = 601975 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 601975 is also equal to 801975 when expressed as a mixed number.

The repeating decimal 80.253 (vinculum notation) has a repeated block length of 1. It is also represented as 80.25333... (ellipsis notation) which equals approximately 80.2533333 (decimal approximation)(*).

The recurring decimal 80.253 can be written as a ratio of two integers having 6019 as the numerator and 75 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.