What is 16.45333... as a Fraction?

16.453 equals 123475 as a fraction.

How do you turn 16.453 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.453 repeating into a fraction, begin writing this simple equation:

n = 16.453 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (45). Multiply both sides by 10³ = 1000.

1000 × n = 16453.3 (equation 2)

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

1000 × n = 16453.3
 100 × n = 16.453
 900 × n = 14808

14808900 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 12 (the GCF - greatest common factor).

n = 14808900 = 14808 ÷ 12900 ÷ 12 = 123475. So,

16.453 = 123475 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 123475 is also equal to 163475 when expressed as a mixed number.

The repeating decimal 16.453 (vinculum notation) has a repeated block length of 1. It is also represented as 16.45333... (ellipsis notation) which equals approximately 16.4533333 (decimal approximation)(*).

The recurring decimal 16.453 can be written as a ratio of two integers having 1234 as the numerator and 75 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.