Why is 1 0 04 0 04

Why is?
This time a rather difficult topic!

On the one hand, sharing in writing is not that easy, even with normal numbers. Lots of mistakes can creep in there.

But if you want to divide decimal numbers, you also have to add the comma, which unfortunately makes the problem a little more complicated.

So: turn off the radio, get out of all chats and concentrate really well! Otherwise you have no chance.
 
       
In this lesson you will learn:
1.How to divide by 10, 100, 1000 etc.
2.How to divide a point number by a natural number.
3.How to divide a point number by another point number.
4.How to divide natural numbers with no remainder.
5.And how you can convert any fraction into a decimal point by dividing it.
 Divide by 10, 100, 1000 etc.
Super easy:

You divide by 10, 100, 1000 etc. (number of steps) by simply shifting the decimal point by the corresponding number of places.

So just like with multiplying, only in the other direction:
 

To the left
or to the right?

Just think about whether the number needs to get smaller or larger.



: 10 is the same as 0.1
: 100 is the same as · 0.01
: 0,1 is the same as 10
: 0,01 is the same as 100


345,6 : 100 = 3,456
67,33 : 100 = 0,6733
4,6 : 1000 = 0,0046
 
Should one go through 0.1; 0.01; Dividing 0.001 etc., the decimal point is shifted in the other direction:
 
0,005 : 0,01 = 0,05
2,34 : 0,1 = 23,4
0,34 : 0,001 = 340
 
Floating point through natural number
You have known how to divide natural numbers by other natural numbers since the third grade.

In the case of decimal numbers, there is now the question of where to put the decimal point in the result. The following appliesNOT the same rule as when multiplying !!!

Rather:Where you exceed the decimal point when dividing, you also put the decimal point in the result!
 
Note:
Where you exceed the decimal point when dividing, you also put the decimal point in the result!









Example:  17,94 : 3 = ???
 
The 3 does not fit into the 1. It does, however, fit into the 17, namely 5 times. So write down the 5.

5 · 3 = 15. Write under the 17. Stay 2.
 
Get the 9 down. BUT ATTENTION! Here we exceed the decimal point. Therefore put the comma in the result NOW!
 
29: 3 goes 9 times. Writing down. 9 · 3 are 27. Write under the 29. Stay again 2.
 
Jerk off the 4. 24: 3 = 8th writing down. 8 · 3 = 24. Down, stay zero, done!
 
Example 2:


2 0 8,2  : 6  = 3 4,7
1 8
0 2 8
0 2 4
0 0 4 2
0 0 4 2
0 0 0 0


Only when you have to get the last 2 down do you exceed the decimal point. Exactly then you put it in the result.
 
Point number through point number
How does the situation change if there is also a decimal point on the right? How do you deal with their commas?

Not at all!

You don't divide by a decimal point !!!
That would be very complicated!
 

Note:
You don't divide by a decimal point!
One moves atboth Pay the comma so that it disappears from the second number.







Instead, you rewrite the task: You move the decimal point for BOTH numbers so that the right number becomes natural, i.e. no longer has a decimal point.
 
Examples:

7,82 : 3,4  =  78,2 : 34   (for a position)
0,592 : 0,04  =  59,2 : 4  (by two places)
65 : 1,6  =  650 : 16      (for a position)
 
Once the task has been rewritten, the division is carried out as we learned above.
 

8,6 4  : 3,6  =
8 6,4  : 3 6  = 2,4
7 2
1 4 4
1 4 4
0 0 0
 Divide natural numbers without a remainder
If you used to divide by a number that didn't come up, you could just write down the rest up to fifth grade.

You can forget that now! From now on it will be shared until the socks smoke! As soon as the natural number is "used up", you put a comma in the result and bring down the ending zeros until the division is finished.

You can do this because you can think of any natural number as a decimal point:

73 = 73,00000
 





In the example on the right, we divide normally until the 3 has been brought down and there is 1 left of 33. The result is 18. In the past we would have written "Rest 1".

From today we will instead put the decimal point in the result, think of the 73 as 73,000 ... and take down ending zeros until the division finally works.
 
Example 2:


5 1  : 8  = 6,3 7 5
4 8
0 3 0
0 2 4
0 0 6 0
0 0 5 6
0 0 0 4 0
0 0 0 4 0
0 0 0 0 0
 Periodic point numbers
When sharing without rest, something unpleasant can happen: it doesn't stop.


1 0  : 9  = 1,1 1 1  ...
0 9
0 1 0
0 0 9
0 0 1 0


It can go on forever. It turns in a circle, the dog bites its own tail.
 
A long lesson !!!! :O{







     
Result: 
One point period one

In such cases we speak of oneperiod.

As soon as there is a residue that has already been there: Do not continue calculating! Because everything will repeat itself as it did before. Instead, the repetition, the period, is marked with a line in the result.
 
Example 2:


2 5  : 6  = 4,1 6 7  
2 4
0 1 0
0 0 6
0 0 4 0
0 0 3 6
0 0 0 4
 
How to convert fractions to decimal numbers
In the lesson "Understanding decimals" we learned how to convert a fraction into a point number - BUT only for fractions with very pleasant denominators such as 4, 5, 8, 20, etc. You can do this by shortening and expanding to tenths, hundredths, etc. . brought and then written as a point number.

 = 
3 · 25
4 · 25
 =   = 0,75
 






Note:
Just divide the numerator by the denominator!
Since we just learned how to divide without remainder, we can now convert ALL fractions to decimal numbers.

Because: A fraction just means, as far as arithmetic is concerneddivided!!!

means: 3 divided by 8.

So we just have to divide numerator by denominator and we get a decimal point! :O)
  
 = 3 : 8 = 0,375
 = 5 : 16 = 0,3125
 = 5 : 6 = 0,83
 = 3 : 11 = 0,27
 = 1 : 7 = 0,142857