What is 10.054545454... as a Fraction?

10.54 equals 55355 as a fraction.

How do you turn 10.54 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.54 repeating into a fraction, begin writing this simple equation:

n = 10.54 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (54), so multiply both sides by 10² = 100.

100 × n = 1054.54 (equation 2)

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

100 × n = 1054.54
  1 × n = 10.54
 99 × n = 1044

104499 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 9 (the GCF - greatest common factor).

n = 104499 = 1044 ÷ 999 ÷ 9 = 55355. So,

10.54 = 55355 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 55355 is also equal to 10355 when expressed as a mixed number.

The repeating decimal 10.54 (vinculum notation) has a repeated block length of 2. It is also represented as 10.545454... (ellipsis notation) which equals approximately 10.5454545454 (decimal approximation)(*).

The recurring decimal 10.54 can be written as a ratio of two integers having 553 as the numerator and 55 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.