What is 74.9888... as a Fraction?

74.98 equals 674990 as a fraction.

How do you turn 74.98 repeating into a fraction?

Detailed Answer:

Step 1: To convert 74.98 repeating into a fraction, begin writing this simple equation:

n = 74.98 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 1 digit in the non-repeating part (9). Multiply both sides by 10² = 100.

100 × n = 7498.8 (equation 2)

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

100 × n = 7498.8
 10 × n = 74.98
 90 × n = 6749

n = 674990 (answer)

74.98 = 674990 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 674990 is also equal to 748990 when expressed as a mixed number.

The repeating decimal 74.98 (vinculum notation) has a repeated block length of 1. It is also represented as 74.9888... (ellipsis notation) which equals approximately 74.988888 (decimal approximation)(*).

The recurring decimal 74.98 can be written as a ratio of two integers having 6749 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.