What is 16.58888... as a Fraction?

16.588 equals 149390 as a fraction.

How do you turn 16.588 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.588 repeating into a fraction, begin writing this simple equation:

n = 16.588 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (58). Multiply both sides by 10³ = 1000.

1000 × n = 16588.8 (equation 2)

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

1000 × n = 16588.8
 100 × n = 16.588
 900 × n = 14930

14930900 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 = 14930900 = 14930 ÷ 10900 ÷ 10 = 149390. So,

16.588 = 149390 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 149390 is also equal to 165390 when expressed as a mixed number.

The repeating decimal 16.588 (vinculum notation) has a repeated block length of 1. It is also represented as 16.58888... (ellipsis notation) which equals approximately 16.5888888 (decimal approximation)(*).

The recurring decimal 16.588 can be written as a ratio of two integers having 1493 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.