Real Numbers
Real Numbers
-Real Numbers are every number.
-Therefore, any number that you can find on the number line.
-Real Numbers have two categories, rational and irrational.
Rational Numbers
-Any number that can be expressed as a repeating or terminating decimal is classified as a rational number
Examples of Rational Numbers
6 is a rational number because it can be expressed as 6.0 and therefore it is a terminating decimal.
-7 ½ is a rational number because it can be expressed as -7.5 which is a terminating decimal.
Examples of Rational Numbers
Square root 25 is a rational number because it can be expressed as 5 or 5.0 and therefore it is a terminating decimal.
2.45 is a rational number because it is a repeating decimal.
Irrational Numbers
-An irrational number is a number that cannot be written as a fraction of two integers.
-Irrational numbers written as decimals are non-terminating and non-repeating.
Note: if a whole number is not a perfect square, then its square root is an irrational number.
Caution!
A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.
Examples of Irrational Numbers
Square root of 21 is an irrational number because it can Not be expressed as a terminating decimal.
0.62622622262222… is an irrational number because it cannot be expressed as a repeating decimal.
Examples of Irrational Numbers
Π (pi)is an irrational number.
Subsets of Rational Numbers
-Natural numbers
-Whole numbers
-Integers
Natural Numbers
Natural Numbers are counting numbers from {1,2,3,4,5,…}
Whole Numbers
Whole numbers are counting numbers from {0,1,2,3,4,5,…}
Integers
Integers include the negative counting numbers: {…,-3,-2,-1,0,1,2,3…}
What Does It Mean?
-The number line goes on forever.
-Every point on the line is a Real number.
-There are no gaps on the number line.
-Between the integers there are countless other numbers. Some of them are rational (fractions, terminating and
-Real Numbers are every number.
-Therefore, any number that you can find on the number line.
-Real Numbers have two categories, rational and irrational.
Rational Numbers
-Any number that can be expressed as a repeating or terminating decimal is classified as a rational number
Examples of Rational Numbers
6 is a rational number because it can be expressed as 6.0 and therefore it is a terminating decimal.
-7 ½ is a rational number because it can be expressed as -7.5 which is a terminating decimal.
Examples of Rational Numbers
Square root 25 is a rational number because it can be expressed as 5 or 5.0 and therefore it is a terminating decimal.
2.45 is a rational number because it is a repeating decimal.
Irrational Numbers
-An irrational number is a number that cannot be written as a fraction of two integers.
-Irrational numbers written as decimals are non-terminating and non-repeating.
Note: if a whole number is not a perfect square, then its square root is an irrational number.
Caution!
A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.
Examples of Irrational Numbers
Square root of 21 is an irrational number because it can Not be expressed as a terminating decimal.
0.62622622262222… is an irrational number because it cannot be expressed as a repeating decimal.
Examples of Irrational Numbers
Π (pi)is an irrational number.
Subsets of Rational Numbers
-Natural numbers
-Whole numbers
-Integers
Natural Numbers
Natural Numbers are counting numbers from {1,2,3,4,5,…}
Whole Numbers
Whole numbers are counting numbers from {0,1,2,3,4,5,…}
Integers
Integers include the negative counting numbers: {…,-3,-2,-1,0,1,2,3…}
What Does It Mean?
-The number line goes on forever.
-Every point on the line is a Real number.
-There are no gaps on the number line.
-Between the integers there are countless other numbers. Some of them are rational (fractions, terminating and