What is 20.4757575... as a Fraction?

20.475 equals 6757330 as a fraction.

How do you turn 20.475 repeating into a fraction?

Detailed Answer:

Step 1: To convert 20.475 repeating into a fraction, begin writing this simple equation:

n = 20.475 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (75) and 1 digit in the non-repeating part (4). Multiply both sides by 10³ = 1000.

1000 × n = 20475.75 (equation 2)

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

1000 × n = 20475.75
  10 × n = 20.475
 990 × n = 20271

20271990 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 3 (the GCF - greatest common factor).

n = 20271990 = 20271 ÷ 3990 ÷ 3 = 6757330. So,

20.475 = 6757330 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 6757330 is also equal to 20157330 when expressed as a mixed number.

The repeating decimal 20.475 (vinculum notation) has a repeated block length of 2. It is also represented as 20.4757575... (ellipsis notation) which equals approximately 20.47575757575 (decimal approximation)(*).

The recurring decimal 20.475 can be written as a ratio of two integers having 6757 as the numerator and 330 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.