What is 96.3555... as a Fraction?

96.35 equals 433645 as a fraction.

How do you turn 96.35 repeating into a fraction?

Detailed Answer:

Step 1: To convert 96.35 repeating into a fraction, begin writing this simple equation:

n = 96.35 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5) and 1 digit in the non-repeating part (3). Multiply both sides by 10² = 100.

100 × n = 9635.5 (equation 2)

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

100 × n = 9635.5
 10 × n = 96.35
 90 × n = 8672

867290 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 2 (the GCF - greatest common factor).

n = 867290 = 8672 ÷ 290 ÷ 2 = 433645. So,

96.35 = 433645 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 433645 is also equal to 961645 when expressed as a mixed number.

The repeating decimal 96.35 (vinculum notation) has a repeated block length of 1. It is also represented as 96.3555... (ellipsis notation) which equals approximately 96.355555 (decimal approximation)(*).

The recurring decimal 96.35 can be written as a ratio of two integers having 4336 as the numerator and 45 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.