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You know that 1/7= 0.bar(142857) Can you...

You know that `1/7= 0.bar(142857)` Can you predict what the decimal expansions of `2/7,3/7,4/7,5/7,6/7` are, without actually doing the long division? If so, how? [Hint : Study the remainders while finding the value of `1/7` carefully.]

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PSEB-NUMBER SYSTEMS-EXAMPLE
  1. You know that 1/7= 0.bar(142857) Can you predict what the decimal expa...

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  2. Is the following statement true of false? Give reasons for your answer...

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  3. Is the following statement true of false? Give reasons for your answer...

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  4. Is the following statement true of false? Give reasons for your answer...

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  5. Find five rational numbers between 1 and 2. We can approach this probl...

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  6. Locate sqrt2 on the number line.

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  7. Locate sqrt3 on the number line.

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

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  9. Show that 3.142678 is a rational number. In other words, express 3.142...

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  10. Show that 0.3333... =0.bar3 can be expressed in the form p/q, where p ...

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  11. Show that 1.272727... =1.bar27 can be expressed in the form p/q , wher...

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  12. Show that 0.2353535... = 0.2bar35 can be expressed in the form p/q, w...

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  13. Find an irrational number between 1/7 and 2/7.

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  14. Check whether 7sqrt5, 7/sqrt5, sqrt2+21, pi-2 are irrational numbers o...

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  15. Add 2sqrt2+ 5sqrt3 and sqrt2- 3sqrt 3.

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  16. Multiply 6sqrt 5 by 2 sqrt5 .

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  17. Divide 8 sqrt15 by 2 sqrt3 .

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  18. Simplify the following expression:- (5+sqrt7)(2+sqrt5)

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  19. Simplify the following expression:- (5+sqrt5)(5-sqrt5)

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  20. Simplify the following expression:- (sqrt3+sqrt7)^2

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  21. Simplify the following expression:- (sqrt11-sqrt7)(sqrt11+sqrt7)

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