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Show that 0. 2353535. . .=0. 2 bar 35can...

Show that `0. 2353535. . .=0. 2 bar 35`can be expressed in the form `p/q`, where p and q are integers and `q!=0`.

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AI Generated Solution

To express \( 0.235353535... \) (or \( 0.2\overline{35} \)) in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \), we can follow these steps: ### Step 1: Let \( x = 0.235353535... \) We start by defining the repeating decimal as a variable: \[ x = 0.235353535... \] ...
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NCERT ENGLISH-NUMBER SYSTEMS-Solved Examples
  1. Show that 0. 3333. . . .=0. bar3can be expressed in the form p/q, wher...

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  2. Locate sqrt(3)on the number line.

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  3. Find the decimal expansions of (10)/3,7/8and 1/7.

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  4. Find five rational numbers between 1 and 2. We can approach this prob...

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  5. Locate sqrt(2)on the number line.

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  6. Are the following statements true or false? Give reasons for your ans...

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  7. Rationalise the denominator of 1/(7+3sqrt(2))

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  8. Simplify (i) 2^(2/3). 2^(1/3) (ii) (3^(1/5))^4 (iii) (7^(1/5))/(7^(1...

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  9. Show that 1. 272727. . .=1. bar 27can be expressed in the form p/q, wh...

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  10. Show that 0. 2353535. . .=0. 2 bar 35can be expressed in the form p/q...

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  11. Visualize the representation of 5. 3 bar7 on the number line upto 5 de...

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  12. Find the irrational number between 1/7and 2/7.

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  13. Add 2sqrt(2)+5sqrt(3) and sqrt(2)-3sqrt(3).

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  14. Check whether 7sqrt(5),7/(sqrt(5)),sqrt(2)+21 ,pi-2are irrational numb...

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  15. Divide 8sqrt(15)and 2sqrt(3).

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  16. Multiply 6sqrt(5)by 2sqrt(5).

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  17. Rationalise the denominator of 1/(sqrt(2))

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  18. Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (...

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  19. Rationalise the denominator of 5/(sqrt(3)-sqrt(5))

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  20. Rationalise the denominator of 1/(2+sqrt(3))

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