Classifying Numbers
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Rational numbers can be written as fractions or terminating decimals, while irrational numbers are non-repeating and non-terminating decimals that cannot be expressed as fractions. The document provides examples of rational numbers like 3/1, 3/2, 1/9, 4, and 7/1000. Examples of irrational numbers given include the square root of 2 and pi, which have non-repeating decimals. The document includes interactive exercises asking the user to identify numbers as rational or irrational.
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Rational numbers are numbers that can be represented as fractions p/q where p and q are integers and q is not equal to 0, such as 2/5 or 4/7. Irrational numbers are numbers that cannot be represented as fractions, such as √2 or √3, and their decimal representations are non-terminating and non-repeating. Real numbers include both rational and irrational numbers and can all be represented as unique points on a number line, with rational numbers having either terminating or non-terminating repeating decimals and irrational numbers having non-terminating, non-repeating decimals.
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Here are the answers with explanations:
(i) True. Every natural number is a whole number. The set of natural numbers is a subset of the set of whole numbers.
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This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as p/q where p and q are integers and q is not equal to 0. Rational numbers include fractions, integers, and natural numbers. The document describes the different types of rational numbers such as positive, negative, and in standard form. It also discusses how to perform operations like addition, subtraction, multiplication, and division on rational numbers. Irrational numbers are defined as real numbers that cannot be expressed as a ratio of integers like the roots of prime numbers or pi.
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This is meant for age group 11 to 14 years.
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Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
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Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
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The document discusses real numbers and their classification. It defines real numbers as any number that can be found on the number line, including rational and irrational numbers. Rational numbers are those that can be written as fractions, with decimal forms that terminate or repeat. Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimal forms. Examples of rational numbers given include integers and fractions, while examples of irrational numbers include π and square roots of non-perfect squares. The document provides examples of classifying numbers as rational or irrational and ordering them on the number line.
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Classifying Numbers
- 1. Classifying Numbers Rational Numbers vs. Irrational Numbers
- 2. A Rational Number: An Irrational Number: • Cannot be written as a simple fraction • Non-terminating decimal (doesn’t end) • Non-repeating decimal (doesn’t repeat in a pattern) Irrational doesn’t mean that it’s crazy! 2
- 3. Examples of Rational Numbers Click on each number to see explanation Can be Can be Can be written as written as written as 7/1000 3/1 3/2 Repeating Already in decimal. Can fraction form be written as Can be 1/9 written as 4 and as 4/1 3
- 4. Examples of Irrational Numbers 4
- 5. More Irrational Numbers Click on each number to see explanation Remember . . . Irrational numbers are non-repeating and non-terminating decimals and cannot be written as a fraction. Non-repeating decimal. Can’t be written as a fraction Non-repeating decimal. Can’t be written as fraction 5
- 6. Try this . . . 6
- 7. Time to practice INCORRECT 0.5 can be written as ½ and so it is rational. Try again! Correct! 0.5 can be written as ½ Good work! 7
- 8. Time to practice 8
- 9. Time to practice CORRECT! -5.060715… non-repeating, non- terminating decimal Good job! INCORRECT -5.060715… appears to be a non- repeating, non- terminating decimal Try again! 9
- 10. Time to practice 10
- 11. Time to practice INCORRECT 2/3 is a fraction and so it is rational. Try again! CORRECT 2/3 is a fraction. Good work! 11
- 12. Time to practice 12
- 13. How many RATIONAL numbers can you find? Find the answer on the next slide 13
- 14. Did you find 6 rational numbers? They are: 14