5th grade
Natural numbers
Basic arithmetic operations
Calculation laws and advantages
Geometry

6th grade
Divisibility of numbers
Factions
Decimal fractions
Angles and angle measures

7th grade
Assignment and rule of three
Calculation of percentage
Rational numbers
Equation and inequation
Probability calculus

8th grade
Function and assignment
Triangles
Quadrangles
Calculation of surfaces
Transformation of terms
Probability calculus

9th grade
The root
Record set of the pythagoras

10th grade
Circle calculation
The cone
Power calculation
Power laws
Exponential function
Logarithm
Trigonometry
Probability calculus

 

Decimal fractions
German system with comma in spite of point

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We can also represent fractions in another form. (Not with a nominator, fraction bar and denominator) We do this, with so called decimal fractions. These are nothing more than a few digits with a comma in a certain place. Whole numbers stand in front of the comma (for example, 1, 2, 3,… , 25,…) the first digit after the comma, ( 25,5 for example) shows the tenth part. This means we have 25 wholes and 5 tenths. The second digit after the comma shows the hundredths (25,54 for example, which means 25 +). The third digit shows the thousandths (25,547 for example, which is 25 +) so on and so forth.

 

We can also transform normal fractions into decimal fractions. We do this, by either shortening or extending the fraction to tenths, hundredths, thousandths etc.

Example: 

 

If this procedure does not work or can only be carried out difficulty, we can help ourselves by using division. Examples here to:

= 5 : 16 = 0,3125

A little more difficult (but not much) is the same procedure with the cycles/periods. A definition of periods: Periods are repeated numbers or numerical order, after the comma for example: 0,33333333333… in this case there are no tenths or hundreds but instead, we have ninths and ninety ninths so on and so forth.

 

Examples of transforming periods:

 

 

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02/09/07