MATH 9SECTION 3.1 WHAT ARERATIONAL NUMBERS
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REVIEW:
Natural Numbers
Numerical values that exist in nature ie: 1, 2, 3, 4, 5, …
Whole Numbers
Number that represent a whole ie: 0, 1, 2, 3, 4, 5, …
Integers
Whole numbers that can be positive or negative
Ie: –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5
Rational Number – Any number that can be writtenas a fraction where both the numerator anddenominator are integers
½ , ¾ , 5/6, –¾, 4/4, 30/1
Note: natural numbers, whole numbers, and integers areall rational numbers as well
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RATIONAL VS IRRATIONAL
Remember: All rational numbers can be written as afraction
Other characteristics of rational numbers:
When written in decimal form R.N. will terminate OR
If they don’t terminate they will have a consistent pattern
Irrational – something that doesn’t make sense
Irrational numbers – can not be written as a fractionwith numerator and denominator as integers
When irrational numbers are in decimal form, they do notterminate and they don’t have a consistent pattern
Ie: (pi has infinite number of decimal places),
1 decimal place
3 decimal places
6 decimal places
Pattern of 2
repeating digits
Pattern of 6
repeating digits
Pattern of 16
repeating digits
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COMMON RATIONAL NUMBERS
Since all R.N. can be written as a fraction, here aresome common R.N.
Numbers with only one decimal place:
Write the decimal place over 10
Numbers with repeating digits:
Write the repeating digit over 9
Numbers that end with quarters:
Write the value over 4
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DRAWING RATIONAL NUMBERS ON A NUMBER LINE
The big number on the left indicates where to start onthe number line
The value of the denominator determines how manyincrements that the distance between two wholenumbers should be cut into
The numerator determines which increment you want
The denominator is 8, so cut thedistance from 1 to 2 into 8 pieces
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EX: DRAW EACH OF THE FOLLOWING RATIONALNUMBERS ON A NUMBER LINE:
This value isbetween 0 and 1
This value isbetween 3 and 4
This value isbetween -2 and -3
Split the increment into 7 parts
Split the increment into 5 parts
Split the increment into 3 parts
Since the value is negative, they areincremented from left to right
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EX: GIVEN EACH PAIR OF RATIONAL NUMBERS, INDICATEWHICH OF THE CHOICES ARE IN BETWEEN THEM
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HOMEWORK:
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