Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Unit Test : Number Systems
Unit Test : Number Systems | Mathematics (Maths) Class 9 PDF Download
Time: 1 hour
M.M.: 30
Attempt all questions.
Question numbers 1 to 5 carry 1 mark each.
Question numbers 6 to 8 carry 2 marks each.
Question numbers 9 to 11 carry 3 marks each.
Question numbers 12 & 13 carry 5 marks each.
Q1: What is the product of a rational and an irrational number? (1 Mark)
(i) Always an integer
(ii)Always a rational number
(iii) Always an irrational number
(iv)Sometimes rational and sometimes irrational
Q2: What is the value of (256)0.16 X (256)0.09? (1 Mark)
(i)4
(ii)16
(iii)64
(iv)256.25
Q3: Add 2√2+ 5√3 and √2 – 3√3. (1 Mark)
Q4: Simplify: (√3+√7) (√3-√7). (1 Mark)
Q5: Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number. (1 Mark)
Q6: Find five rational numbers between 3/5 and 4/5. (2 Marks)
Q7: Rationalise the denominator of 1/[7+3√3]. (2 Marks)
Q.8: Simplify: (2 Marks)
(i) 72/3.71/5
(ii) 101/2/101/4
Q9: Find three different irrational numbers between the rational numbers 5/7 and 9/11. (3 Marks)
Q.10: Represent √(9.3) on the number line. (3 Marks)
Q11: Locate √3 on the number line. (3 Marks)
Q12: Find the decimal expansions of 10/3, 7/8 and 1/7. (5 Marks)
Q13: What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer. (5 Marks)
You can find the solutions of this Unit Test here: Unit Test (Solution) : Number Systems
The document Unit Test : Number Systems | Mathematics (Maths) Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Unit Test : Number Systems - Mathematics (Maths) Class 9
| 1. What are the different types of number systems used in mathematics? |  |
Ans. The primary types of number systems are the decimal system (base 10), binary system (base 2), octal system (base 8), and hexadecimal system (base 16). Each system has its own base and is used in various applications, with the decimal system being the most common for everyday counting, binary for computer programming, octal for certain computing systems, and hexadecimal for representing large binary numbers in a more readable form.
| 2. How do you convert a binary number to decimal? | |
Ans. To convert a binary number to decimal, you need to multiply each digit by 2 raised to the power of its position, starting from 0 on the right. Then, sum all the results. For example, the binary number 1011 converts to decimal as follows: (1×2^3) + (0×2^2) + (1×2^1) + (1×2^0) = 8 + 0 + 2 + 1 = 11 in decimal.
| 3. What is the importance of understanding number systems in computer science? | |
Ans. Understanding number systems is crucial in computer science because computers operate using binary code. Knowledge of different number systems helps in programming, data representation, and understanding how computers perform calculations and store data. This foundational knowledge aids in developing algorithms and optimizing code efficiency.
| 4. How can I practice converting numbers between different systems? | |
Ans. You can practice converting numbers between different systems by using online conversion tools, worksheets, or by creating flashcards with numbers in one system on one side and their equivalents in another system on the other side. Additionally, programming exercises that require you to implement conversion algorithms can also enhance your skills.
| 5. What are common mistakes to avoid when working with number systems? | |
Ans. Common mistakes include miscalculating the place values, forgetting to carry over when necessary, and confusing the base of the number system being used. It's also important to double-check conversions, as small errors can lead to incorrect results, especially in programming and mathematical calculations.
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