Identify rational and irrational numbers
Key notes :
Definitions:
Rational Numbers: Numbers that can be expressed as a fraction of two integers (a/b), where b is not zero.
Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers and have non-terminating, non-repeating decimal expansions.
Examples:
Rational Numbers: 2, -5, 3/4, -1.25, √9 (which is 3), etc.
Irrational Numbers: √2, π (pi), √5, e (Euler’s number), 2.15264123…… etc.
Characteristics:
Rational numbers either terminate or repeat in their decimal form.
Irrational numbers have decimal expansions that neither terminate nor repeat.
Identifying Methods:
Decimal Form: Convert the number to decimal form. If it terminates or repeats, it’s rational; if not, it’s irrational.
Square Root Test: If a number’s square root is not a perfect square, it’s irrational.
Closure Properties:
Rational numbers are closed under addition, subtraction, multiplication, and division (except division by zero).
Adding or multiplying a rational number with an irrational number results in an irrational number.
Importance:
Understanding rational and irrational numbers helps in calculations involving precise measurements and theoretical concepts in mathematics and sciences.
Learn with an example
is 2/10 an irrational number?
- yes
- no
2/10 is a fraction. So, 2/10 is not an irrational number.
Which of the following describes √2?
Select all that apply.
- irrational number
- rational number
√2 (which is 1.41421…) cannot be written as a fraction, a terminating decimal, or a repeating decimal. So, √2 is not a rational number.
Since √2 is not a rational number, it is an irrational number.
There is one correct answer choice. √2 is an irrational number.
Which of the following describes 5/6?
Select all that apply.
- irrational number
- rational number
5/6 is a fraction. So, 5/6 (which is 5/6 ) is a rational number.
Since 5/6 is a rational number, it is not an irrational number.
There is one correct answer choice. 5/6 is a rational number.
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