Class 9 Practice Set 2.1 Real Numbers Chapter 2| 9th Maths 1 | Std 9 | Algebra New Syllabus |SSC
Yogesh Sir's Backbenchers・29 minutes read
Chapter two of the Standard Nath Maths and Algebra textbook explores the concept of Real Numbers, including natural, whole, integers, and rational numbers, with a focus on terminating and non-terminating recurring decimals in division. Examples and practical instructions are provided to help learners understand how to calculate and convert rational numbers into decimal form accurately.
Insights
- Rational numbers encompass natural, whole, and integer numbers, with terminating decimals ending at a certain point and non-terminating recurring decimals repeating indefinitely.
- Converting rational numbers to decimal form involves factorizing the denominator to identify terminating or non-terminating recurring types, utilizing factors of two or five for termination, and other factors for non-termination, emphasizing the importance of division and tables for accuracy and clarity in the conversion process.
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Recent questions
What are natural numbers?
Numbers used for counting from one to infinity.
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Summary
00:00
Understanding Real Numbers in Mathematics
- Chapter number two of Standard Nath Maths and Algebra is Real Numbers, focusing on simple questions but challenging concepts.
- Natural numbers (n) are those used for counting, starting from one to infinity.
- Whole numbers (w) include natural numbers and zero, with no decimal points.
- Integers (Inti Jars) encompass all positive, negative, and zero numbers without decimals.
- Rational numbers (q) are numbers in the form of p/q, where p and q are integers and q is not zero.
- Real numbers comprise all numbers representable on a number line, including natural, whole, integer, and rational numbers.
- Natural numbers are a subset of whole numbers, which are a subset of integers, which are a subset of rational numbers.
- Terminating decimal numbers end after a certain point, while non-terminating recurring decimals repeat indefinitely.
- Classifying rational numbers into terminating or non-terminating recurring types involves dividing and checking for repeating patterns or using prime factorization of the denominator.
- The decimal form of rational numbers like 13/5 is determined by factors of the denominator, with factors of 2 or 5 indicating a terminating type, while other factors suggest a non-terminating recurring type.
13:31
Factors Determine Terminating or Recurring Decimals
- Non-terminating recurring type is the result if factors other than two or five are present in a non-terminating number.
- To determine the denominator in 29/16, factorize 16 as 2 * 2 * 2 * 2.
- Factors are found by multiplying numbers like 2 * 8 to identify factors like twos or fives.
- For 17/125, the denominator 125 is factorized to reveal only twos and fives, indicating a terminating type.
- The denominator in 11/6 is 6, with factors 2 * 3, leading to a terminating type.
- Non-terminating recurring type is the outcome when factors beyond twos or fives are present.
- To convert 127/200 into decimal form, divide 127 by 200, resulting in 0.63.
- Multiplying both numerator and denominator by the same number, like 5 in this case, can simplify division to obtain 0.635.
- For 25/99, division yields 0.2525, showcasing a recurring decimal pattern.
- Understanding division and utilizing tables aids in converting rational numbers into decimal form, ensuring clarity and accuracy.
25:58
"Sub-cutting numbers to reveal patterns"
- The process involves sub-cutting numbers and adding extra zeros to obtain specific results, such as 7 8 56 and 7 5 35.
- By sub-cutting 7 for 28 and adding zeros, a pattern emerges where 20 is repeated, leading to the final result of 2857.
- The division process is explained with examples, like 4 divided by 5 resulting in 0.8, emphasizing the absence of a decimal point or bar when the division ends.
- Practical instructions are given for solving division problems, like 17 divided by 8 resulting in 2.125, encouraging viewers to pause the video and solve the questions themselves for better understanding.
