money serial number lookup for value trinary

The Star Note Lookup received its latest round of updates a few weeks ago which should improve understandability, general look-and-feel, and add a few features. As more collectors come to My Currency Collection for reference information, the more motivated I am to provide easier-to-use tools and more in-depth data. The Star Note Lookup and other reference pages have continually grown in popularity. Building the first version of the Star Note Lookup made searching star note production numbers much easier than wading through massive tables. Many were in tatters and most were from full print runs, but it was always a thrill to hope the note was from a run of less than 640,000 notes. A single pack of 100 $1 notes sometimes yielded as many as five star notes (with the exception one uncirculated pack of star notes). My main currency interest was star notes, because I could grow my collection on the cheap by searching from packs of circulates notes. I was a beginner collector and beginner web developer. Something very similar happens with trinary fractions, but the important digit here is 2 rather than 9.You may not know this, but the Star Note Lookup was the birth of this website. In fact, for any decimal number that terminates, we can write the same number by subtracting 1 from the final digit and adding recurring 9s. For example, the same thing happens with 0.035: We can prove this using the geometric series formula from earlier. It is just a different way to write the number 1. Notice that 0.999 recurring isn't approximately equal to 1, it is exactly equal to 1. This may seem contradictory, but the reason is that 0.999 recurring is equal to 1. With decimal fractions, if we multiply 0.333 recurring by 3, we don't get 1, we get 0.999 recurring. This can be proved similarly (in this case a is 2/9, r is 1/9, and (1 - r) is 8/9). This proves that 0.111 recurring, in base 3, is equal to a half.Īs another example, a quarter has the base 3 value of 0.020202 recurring. The value (1 - r) is equal to 2/3, so the sum of the series is: In our case, a is 1/3 and r is also 1/3, so the formula is valid. This formula is valid if r is less than 1. This is an infinite geometric series, and its sum can be written as: This can be written in terms of powers of 1/3, like this: This can be shown quite easily, by expanding out the terms in 0.111.: For example, a half in trinary is 0.111 recurring. However, there are recurring fractions in trinary too. In the trinary system, a third is simply expressed as 0.1. The simplest example is a third which is expressed as 0.333 recurring. In the decimal system, many rational numbers have to be expressed as recurring fractions. The number is equal to 2 thirds, plus 1 ninth, which simplifies to 7/9. The first digit after the point represents thirds of a unit, the second represents ninths, and the third represents twenty-sevenths. In trinary, we can also use a decimal point (or rather, a trinary point). That is equal to 125/1000, which of course is 1/8. The number is equal to 1 tenth, plus 2 hundredths, plus 5 thousandths. For example the decimal fraction 0.125 represents this value: In base ten, we use a decimal point to represent fractions. 10 is made up of 1 times 9 plus 1 times 1.

So for example, 5 is made up of 1 times 3 plus 2 times 1. Here are the numbers 0 to 10 (denary) in base 3: The base 3 value is calculated like this:īase 10 uses the digits 0 to 9, but base 3 uses the digits 0, 1 and 2. The value 142 in base 10 is represented like this in base 3: These values go up in powers of 3 - in other words, the value of each column triples as we move to the left. This means that the least significant digit represents 1, next represents 3's, then 9's, 27's, 81's and so on. This is a deep dive into trinary numbers that should help if you want to fully appreciate the Cantor set. Trinary numbers, in particular trinary fractions, are very useful for analysing the set.

The Cantor set is based on an iterative process of dividing intervals into three parts. Why study these numbers? Well, one important reason is to understand the Cantor set.

This article is about trinary numbers (sometimes called ternary numbers). And if you have ever done any computer programming you will also be familiar with base 2 numbers (binary). We are all familiar with base 10 numbers (denary).

Money serial number lookup for value trinary