What is 15.43333... as a Fraction?

15.433 equals 46330 as a fraction.

How do you turn 15.433 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.433 repeating into a fraction, begin writing this simple equation:

n = 15.433 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (43). Multiply both sides by 10³ = 1000.

1000 × n = 15433.3 (equation 2)

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

1000 × n = 15433.3
 100 × n = 15.433
 900 × n = 13890

13890900 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 30 (the GCF - greatest common factor).

n = 13890900 = 13890 ÷ 30900 ÷ 30 = 46330. So,

15.433 = 46330 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 46330 is also equal to 151330 when expressed as a mixed number.

The repeating decimal 15.433 (vinculum notation) has a repeated block length of 1. It is also represented as 15.43333... (ellipsis notation) which equals approximately 15.4333333 (decimal approximation)(*).

The recurring decimal 15.433 can be written as a ratio of two integers having 463 as the numerator and 30 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.