What is 25.105454... as a Fraction?

25.1054 equals 6904275 as a fraction.

How do you turn 25.1054 repeating into a fraction?

Detailed Answer:

Step 1: To convert 25.1054 repeating into a fraction, begin writing this simple equation:

n = 25.1054 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (54) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁴ = 10000.

10000 × n = 251054.54 (equation 2)

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

10000 × n = 251054.54
  100 × n = 25.1054
 9900 × n = 248544

2485449900 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 36 (the GCF - greatest common factor).

n = 2485449900 = 248544 ÷ 369900 ÷ 36 = 6904275. So,

25.1054 = 6904275 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 6904275 is also equal to 2529275 when expressed as a mixed number.

The repeating decimal 25.1054 (vinculum notation) has a repeated block length of 2. It is also represented as 25.10545454... (ellipsis notation) which equals approximately 25.105454545454 (decimal approximation)(*).

The recurring decimal 25.1054 can be written as a ratio of two integers having 6904 as the numerator and 275 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.