What is 17.2966... as a Fraction?

17.296 equals 5189300 as a fraction.

How do you turn 17.296 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.296 repeating into a fraction, begin writing this simple equation:

n = 17.296 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (29). Multiply both sides by 10³ = 1000.

1000 × n = 17296.6 (equation 2)

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

1000 × n = 17296.6
 100 × n = 17.296
 900 × n = 15567

15567900 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 3 (the GCF - greatest common factor).

n = 15567900 = 15567 ÷ 3900 ÷ 3 = 5189300. So,

17.296 = 5189300 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 5189300 is also equal to 1789300 when expressed as a mixed number.

The repeating decimal 17.296 (vinculum notation) has a repeated block length of 1. It is also represented as 17.29666... (ellipsis notation) which equals approximately 17.2966666 (decimal approximation)(*).

The recurring decimal 17.296 can be written as a ratio of two integers having 5189 as the numerator and 300 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.