What is 62.27777... as a Fraction?

62.277 equals 112118 as a fraction.

How do you turn 62.277 repeating into a fraction?

Detailed Answer:

Step 1: To convert 62.277 repeating into a fraction, begin writing this simple equation:

n = 62.277 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7) and 2 digits in the non-repeating part (27). Multiply both sides by 10³ = 1000.

1000 × n = 62277.7 (equation 2)

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

1000 × n = 62277.7
 100 × n = 62.277
 900 × n = 56050

56050900 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 50 (the GCF - greatest common factor).

n = 56050900 = 56050 ÷ 50900 ÷ 50 = 112118. So,

62.277 = 112118 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 112118 is also equal to 62518 when expressed as a mixed number.

The repeating decimal 62.277 (vinculum notation) has a repeated block length of 1. It is also represented as 62.27777... (ellipsis notation) which equals approximately 62.2777777 (decimal approximation)(*).

The recurring decimal 62.277 can be written as a ratio of two integers having 1121 as the numerator and 18 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.