What is 4.25757575... as a Fraction?

4.2575 equals 28166 as a fraction.

How do you turn 4.2575 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.2575 repeating into a fraction, begin writing this simple equation:

n = 4.2575 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (75) and 2 digits in the non-repeating part (25). Multiply both sides by 10⁴ = 10000.

10000 × n = 42575.75 (equation 2)

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

10000 × n = 42575.75
  100 × n = 4.2575
 9900 × n = 42150

421509900 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 150 (the GCF - greatest common factor).

n = 421509900 = 42150 ÷ 1509900 ÷ 150 = 28166. So,

4.2575 = 28166 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 28166 is also equal to 41766 when expressed as a mixed number.

The repeating decimal 4.2575 (vinculum notation) has a repeated block length of 2. It is also represented as 4.25757575... (ellipsis notation) which equals approximately 4.257575757575 (decimal approximation)(*).

The recurring decimal 4.2575 can be written as a ratio of two integers having 281 as the numerator and 66 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.