What is 102.25333... as a Fraction?

102.253 equals 766975 as a fraction.

How do you turn 102.253 repeating into a fraction?

Detailed Answer:

Step 1: To convert 102.253 repeating into a fraction, begin writing this simple equation:

n = 102.253 (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 = 102253.3 (equation 2)

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

1000 × n = 102253.3
 100 × n = 102.253
 900 × n = 92028

92028900 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 = 92028900 = 92028 ÷ 12900 ÷ 12 = 766975. So,

102.253 = 766975 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 766975 is also equal to 1021975 when expressed as a mixed number.

The repeating decimal 102.253 (vinculum notation) has a repeated block length of 1. It is also represented as 102.25333... (ellipsis notation) which equals approximately 102.2533333 (decimal approximation)(*).

The recurring decimal 102.253 can be written as a ratio of two integers having 7669 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.