What is 24.2636363... as a Fraction?

24.263 equals 2669110 as a fraction.

How do you turn 24.263 repeating into a fraction?

Detailed Answer:

Step 1: To convert 24.263 repeating into a fraction, begin writing this simple equation:

n = 24.263 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (63) and 1 digit in the non-repeating part (2). Multiply both sides by 10³ = 1000.

1000 × n = 24263.63 (equation 2)

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

1000 × n = 24263.63
  10 × n = 24.263
 990 × n = 24021

24021990 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 = 24021990 = 24021 ÷ 9990 ÷ 9 = 2669110. So,

24.263 = 2669110 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 2669110 is also equal to 2429110 when expressed as a mixed number.

The repeating decimal 24.263 (vinculum notation) has a repeated block length of 2. It is also represented as 24.2636363... (ellipsis notation) which equals approximately 24.26363636363 (decimal approximation)(*).

The recurring decimal 24.263 can be written as a ratio of two integers having 2669 as the numerator and 110 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.