What is 32.3... as a Fraction?

32.3 equals 973 as a fraction.

How do you turn 32.3 repeating into a fraction?

Detailed Answer:

Step 1: To convert 32.3 repeating into a fraction, begin writing this simple equation:

n = 32.3 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3), so multiply both sides by 10¹ = 10.

10 × n = 323.3 (equation 2)

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

10 × n = 323.3
 1 × n = 32.3
 9 × n = 291

2919 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 = 2919 = 291 ÷ 39 ÷ 3 = 973. So,

32.3 = 973 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 973 is also equal to 3213 when expressed as a mixed number.

The repeating decimal 32.3 (vinculum notation) has a repeated block length of 1. It is also represented as 32.333... (ellipsis notation) which equals approximately 32.33333 (decimal approximation)(*).

The recurring decimal 32.3 can be written as a ratio of two integers having 97 as the numerator and 3 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.