What is 100.25333... as a Fraction?

100.253 equals 751975 as a fraction.

How do you turn 100.253 repeating into a fraction?

Detailed Answer:

Step 1: To convert 100.253 repeating into a fraction, begin writing this simple equation:

n = 100.253 (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 = 100253.3 (equation 2)

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

1000 × n = 100253.3
 100 × n = 100.253
 900 × n = 90228

90228900 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 = 90228900 = 90228 ÷ 12900 ÷ 12 = 751975. So,

100.253 = 751975 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 751975 is also equal to 1001975 when expressed as a mixed number.

The repeating decimal 100.253 (vinculum notation) has a repeated block length of 1. It is also represented as 100.25333... (ellipsis notation) which equals approximately 100.2533333 (decimal approximation)(*).

The recurring decimal 100.253 can be written as a ratio of two integers having 7519 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.