What is 4.2454545454545... as a Fraction?

4.245 equals 467110 as a fraction.

How do you turn 4.245 repeating into a fraction?

Detailed Answer:

Step 1: To convert 4.245 repeating into a fraction, begin writing this simple equation:

n = 4.245 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (45) and 1 digit in the non-repeating part (2). Multiply both sides by 10³ = 1000.

1000 × n = 4245.45 (equation 2)

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

1000 × n = 4245.45
  10 × n = 4.245
 990 × n = 4203

4203990 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 = 4203990 = 4203 ÷ 9990 ÷ 9 = 467110. So,

4.245 = 467110 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 467110 is also equal to 427110 when expressed as a mixed number.

The repeating decimal 4.245 (vinculum notation) has a repeated block length of 2. It is also represented as 4.2454545... (ellipsis notation) which equals approximately 4.24545454545 (decimal approximation)(*).

The recurring decimal 4.245 can be written as a ratio of two integers having 467 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.