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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 `2/7x3/7,4/7,5/7,6/7` are without actually doing the long division? If so how?

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The correct Answer is:
`0. bar (85714)`
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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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SWAN PUBLICATION-NUMBER SYSTEMS-EXERCISE 1.3
  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. Write the following in decimal form and say what kind of decimal expan...

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

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

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

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

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

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

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

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

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

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

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  14. Write three numbers whose decimal expansions are non-terminating non-r...

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

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

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  17. Classify the number as rational or irrational sqrt (225)

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

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

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  20. Classify the following number as rational or irrational : 1.1010010001...

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