What is 75.18888... as a Fraction?

75.188 equals 676790 as a fraction.

How do you turn 75.188 repeating into a fraction?

Detailed Answer:

Step 1: To convert 75.188 repeating into a fraction, begin writing this simple equation:

n = 75.188 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (18). Multiply both sides by 10³ = 1000.

1000 × n = 75188.8 (equation 2)

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

1000 × n = 75188.8
 100 × n = 75.188
 900 × n = 67670

67670900 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 10 (the GCF - greatest common factor).

n = 67670900 = 67670 ÷ 10900 ÷ 10 = 676790. So,

75.188 = 676790 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 676790 is also equal to 751790 when expressed as a mixed number.

The repeating decimal 75.188 (vinculum notation) has a repeated block length of 1. It is also represented as 75.18888... (ellipsis notation) which equals approximately 75.1888888 (decimal approximation)(*).

The recurring decimal 75.188 can be written as a ratio of two integers having 6767 as the numerator and 90 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.