What is 74.13333... as a Fraction?

74.133 equals 111215 as a fraction.

How do you turn 74.133 repeating into a fraction?

Detailed Answer:

Step 1: To convert 74.133 repeating into a fraction, begin writing this simple equation:

n = 74.133 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 74133.3 (equation 2)

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

1000 × n = 74133.3
 100 × n = 74.133
 900 × n = 66720

66720900 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 60 (the GCF - greatest common factor).

n = 66720900 = 66720 ÷ 60900 ÷ 60 = 111215. So,

74.133 = 111215 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 111215 is also equal to 74215 when expressed as a mixed number.

The repeating decimal 74.133 (vinculum notation) has a repeated block length of 1. It is also represented as 74.13333... (ellipsis notation) which equals approximately 74.1333333 (decimal approximation)(*).

The recurring decimal 74.133 can be written as a ratio of two integers having 1112 as the numerator and 15 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.