Real Numbers Two Marks Questions

9th Standard

    Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Express the following in the form  \({p\over q},\)  where p and q are integers and q \(\ne\) 0.
    \(0.2\overline{45}\)

  2. Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
    \({17\over 200}\)

  3. Express the following in the form 3n: 243

  4. Use a fractional index to write \(\left( 5\sqrt { 125 } \right) ^{ 7 }\)

  5. Express the surds in the simple form \(\sqrt { 27 } \)

  6. Express the surds in the simple form \(\sqrt [ 3 ]{ 128 } \)

  7. Find any five rational numbers between
    (i) \(\frac { 1 }{ 4 } \) and \(1\over 5\)
    (ii) 0.1 and 0.11
    (iii) -1 and -2

  8. Convert the following decimal numbers in the form of \(\frac { p }{ q } (p,q\in Z\quad and\quad q\neq 0)\)
    (i) \(0.\overline { 3 } \)
    (ii) \(2.12\overline { 4 } \)
    (iii) \(0.4\overline { 5 } \)
    (iv) \(0.\overline { 568 } \)

  9. Find whether x and y are rational or irrational in the following
    (i) a = 2 + \(\sqrt { 3 } \) , B = 2 - \(\sqrt { 3 } \) ; x = a + b,Y = a+ b
    (ii) a = \(\sqrt { 2 } \)  + 7, B = \(\sqrt { 2 } \) - 7 ; x = a + b, Y = a - b
    (iii) a = \(\sqrt { 75 } \), b = \(\sqrt { 3 } \), x = ab, y = \(\frac { a }{ b } \)
    (iv) a = \(\sqrt { 18 } \), b = \(\sqrt { 3 } \), x = ab, y = \(\frac { a }{ b } \)

  10. Verify that 1 = \(0.\overline { 9 } \)

  11. Convert the following rational numbers into decimal
    (i) \(3\over 4\)
    (ii) \(5\over 8\)
    (iii) \(9\over 25\)

  12. Can we write 0.25 as 0.250000 ...? Can a terminating decimal be written as a recurring decimal?

  13. We used to write \(\pi\) as \(\frac{22}{7}.\) Can we say \(\pi\) is a rational number?

  14. Create a word problem whose solution is an irrational number.

  15. Find any 3 irrational numbers between 0.12 and 0.13.

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