1. Write the decimal form of the given fractions:
(i) 42/100
(ii) 327/500
(iii) 3 + 3/8
(iv) 5/6
(v) 1/5
(vi) 1/7
(vii) 2/13
(viii) 11/17
2. If 'a' is a positive rational number and 'n' is a positive integer greater than 1, prove that a^n is a raional number.
3. Find three rational numbers lying between 0 and 0.1. Find twenty rational numbers between 0and 0.1. Write a method to find weather a number is a rational numbers between 0 and 0.1.
4. Complete the following:
(i) Every point on the number line corresponds to a ______ number which may be either _____ or _____.
(ii) The decimal expansion of any irrational number is neither ______ nor _______.
(iii) The decimal representation of the rational number 8/27 is _______.
(iv) 0 is ______ number.
5. Which of the following rational numbers have the terminating decimal representation? (find without dividing actually)
(i) 3/5
(ii) 7/20
(iii) 2/13
(iv) 27/40
(v) 133/125
(vi) 23/7
6. You have seen that under √2 is not a rational number. Prove that √ 2 + 2 is not a rational number.
7. Prove that 3 √3 is not a rational number.
8. Show that 3 √6 is not a rational number.
9. Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers.
(i) √4
(ii) 3√8
(iii) √1.44
(iv) √(9/27)
(v) -√0.64
(vi) √100
10. In the following equations, find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers:
(i) x2 = 5
(ii) y2 = 9
(iii) z2 = 0.04
(iv) u2 = 17/4
(v) v2 = 3
(vi) w2 = 27
11. Give an example to show that the product of a rational number and an irrational number may be a rational number.
12. State with reason which of the following are surds and which are not:
(i) √5 × √10
(ii) √8 × √6
(iii) √27 × √3
(iv) √16 × √4
(v) 5√8 × 2√6
(vi) √100 × √5
(vii) √100 × √2
(viii) 6√2 × 9√3
(ix) √120 × √45
(x) √15 × √6
13. Give two examples to show that the product of two irrational number may be a rational number.
14. Find the value of √5 correct to two places of √5 decimal.
15. Prove that √3 - √2 is irrational.
16. Prove that √3 + √5 is an irrational number.
17. Find weather the given numbers are rational or irrational:
(i) (√2 + 2)2
(ii) (2 - √2)(2 + √2)
(iii) (√2 + √3)2
(iv) 6/3√2
18. Prove that
(i) 2 + √3 is not a rational number.
(ii) 3√7 is not a rational number.
19. Find weather the given numbers are rational or irrational:
(i) (3 + √2)2
(ii) (3 - √3)(3 + √3)
(iii) 6/2√3
20. Find two rational numbers lying between √2 and √3
21. Express 7/64 as a decimal fraction.
22. Express 12/125 as a decimal fraction.
23. Express 451/13 as a decimal fraction.
Conclusion
If you love the important questions, you can check the website NCERT Class 10 to get more important questions for class 10.I hope you love the "Important Questions For Class 10 Maths Chapter 1" by NCERT Class 10.
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