What is 9.120333... as a Fraction?

9.1203 equals 273613000 as a fraction.

How do you turn 9.1203 repeating into a fraction?

Detailed Answer:

Step 1: To convert 9.1203 repeating into a fraction, begin writing this simple equation:

n = 9.1203 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 3 digits in the non-repeating part (120). Multiply both sides by 10⁴ = 10000.

10000 × n = 91203.3 (equation 2)

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

10000 × n = 91203.3
 1000 × n = 9.1203
 9000 × n = 82083

820839000 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 = 820839000 = 82083 ÷ 39000 ÷ 3 = 273613000. So,

9.1203 = 273613000 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 273613000 is also equal to 93613000 when expressed as a mixed number.

The repeating decimal 9.1203 (vinculum notation) has a repeated block length of 1. It is also represented as 9.120333... (ellipsis notation) which equals approximately 9.12033333 (decimal approximation)(*).

The recurring decimal 9.1203 can be written as a ratio of two integers having 27361 as the numerator and 3000 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.