Title

Way back when numbers were first discussed, you learned the basic information about numbers in Japanese. However, the Sino-Japanese numbering system can go much farther. This lesson will also consider things not mentioned before such as decimal fractions. 

Decimals, 小数しょうすう, aren't difficult to make at all in Japanese. First, you need a number before the decimal point, which is simply read out as 点. The actual name for decimal point is 小数点. If you have zero before the decimal point, then you should say ゼロ・れい・まる. If you have a full number before the decimal point, you should say it correctly. So, if there is 300 before the decimal point, say さんびゃく. After the decimal point, you can simply read out the numbers. So, 4.56757 = よん てん ご ろく なな ご なな.

 Decimal Fractions

As you can imagine, this is not the traditional way of dealing with decimal values. Decimal fractions, which break up things by negative powers and referred to in simple English as tenths, hundredths, etc. place, are represented in Japanese with a set of decimal fraction units that stand for each place from the decimal point and back.

This seems easy enough, right? Sadly, Japanese doesn't make this 100% straight-forward. There are two different decimal fraction systems in use in Japan today. They are not completely interchangeable and are used in their respective situations.  

 First Decimal Fraction System

The first decimal fraction system has many units, but practical use ends at 10-2. Even 厘 is not that common. This system is used in batting averages, idioms, etc. Given how important baseball and set expressions are, remembering four small things isn't that bad. The chart below, though, lists all of the possible units in this system for completeness. 

1. 七分袖
　 Three-quarter sleeves/Sleeves 7/10 the size of a long sleeve.

Second Decimal Fraction System

The second system is not all that different. This one is far shorter and is only used up until 10-5. This is mainly due to the fact that it is used for showing discounts, and prices don't need to be exact as say a scientific finding. This system introduces a different unit for 10-1 and pushes the others from the first system down a power. Realistically, you would never need to go past 分.

2. 五分五分の確率
    Even odds

3. 九分くぶ九厘くりん
     Basically 99% chance, this is used to mean that something is basically so.

4. あの小旅行しょうりょこうでの往いきの汽車のなかの気楽な対話は、その八九分を隣りのお喋しゃべりや小さな妹たちに負おうていたものだとわかった。
I realized that our carefree dialogue on that brief train journey was largely due to the chatterbox behind us and the two little sisters. 

Reading Note: 八九分 is read as はっくぶ and literally means 80, 90%, but it is used to mean "largely".  

5. 九分九厘勝てる。
    We'll almost certainly be able to win.   

Reading Note: 9割 is always read as きゅうわり.  Also, no one says よわり. It's よんわり.

Percentage

Hopefully you know that .5 = 50%. So, how exactly do you express percentage in Japanese? Thankfully, it's the same as in English. You just have a number and パー(セント)・％.

6. 4.5%
     よん てん　ご　パー(セント) 

 Fractions

  For a fraction (分数ぶんすう) take a number, add "分の" and follow it with another number. This creates phrases such as "三分の二" meaning "two of three parts" or "two thirds".　

7. ケーキの四分の一
    A quarter/fourth of the cake.

8. 五分の六
    Six fifths

Vocabulary Note: Improper fraction in Japanese is "仮分数かぶんすう".　

Reading Note: 1/4th is always read as よんぶんのいち. 

大字 are formal 漢字 for numbers created to prevent counterfeiting. That sounds like a noble thing to do, but for those that don't like complicated for simple things, they can be annoying additional characters for things you already know. Thankfully, most have become obsolete, so you will only be introduced to the ones pertaining to Japan today. 

The only ones that you are responsible for knowing are  1 (壱), 2  (弐), 3 (参), 10 (拾), and 10,000 (萬). The latter is not actually used on currency anymore in Japan, but it does have unofficial usage. 

Japanese, with the aid of Sino-Japanese numerals, can be used to count all of the particles of sand on the Earth with greater success. Again, in Japanese big numbers are grouped into powers of four. We stopped in the first lesson concerning numbers at 10^12 (trillion), 兆.

Now, you'll get to see the limit of this system, which is 10^68 until some genius decides to add to this insane list. By no means should you remember any of this as even I only remember a few of these on the spot, but it is some more frivolous and trivial knowledge for fellow Japanese nerds that want to know more about something than the average Japanese speaker. There is some good out of this seemingly nonsensical information. You get to an uncommon reading of 京. You also get to see a weird usage of 不可思議.

なゆた is actually a rather fun word that happens to be used practically to refer to an endless quantity. It sounds fitting, but at look at this system, it is somewhat a misnomer. Well, it's not as bad as the native equivalent of such a concept which treats 千ち and 万よろず as numerous.  

If you never remember 秭, don't feel bad. If you tried to use this in practical use--how it would be practical is beyond reason--people will probably think you meant 一助 or that you just made an error.