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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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MBD-Number Systems-Exercise
  1. Write the following in decimal form and say what kind of decimal expan...

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  2. Write the following in decimal form and say what kind of decimal expan...

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  3. You know that 1/7= 0.bar(142857) Can you predict what the decimal expa...

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  4. Express the following in the form p/q , where p and q are integers and...

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  5. Express the following in the form p/q, where p and q are integers and ...

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  6. Express the following in the form p/q , where p and q are integers and...

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  7. Express 0.99999....... in the form P/q. Are you surprised by your answ...

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  8. What is the maximum number of digits in the repeating block of digits ...

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  9. Look at several examples of rational numbers in the form P/q(q ne 0), ...

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  10. Write three numbers whose decimal expansions are nonterminating nonrec...

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  11. Find three different irrational numbers between the rational numbers 5...

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  12. Classify the following number as rational or irrational : sqrt23

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  13. Classify the following numbers as rational or irrational : sqrt225.

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  14. Classify the following number as rational or irrational : 0.3796

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  15. Classify the following number as rational or irrational : 7.478478...

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  16. Classify the following numbers as rational or irrational : 1.101001000...

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

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  18. Find the decimal expansion of : 1/7.

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

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

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