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anonymous

  • one year ago

Find a rational number and an irrational number that are between 5.2 and 5.5. Include the decimal approximation of the irrational number to the nearest hundredth.

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  1. anonymous
    • one year ago
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    this si the last question.

  2. Michele_Laino
    • one year ago
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    we can write this: \[\Large 5.2 = \frac{{52}}{{10}},\quad 5.5 = \frac{{55}}{{10}}\]

  3. anonymous
    • one year ago
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    okay

  4. Michele_Laino
    • one year ago
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    so a rational number between 5.2 and 5.5 can be: \[\Large \frac{{54}}{{10}} = 5.4\]

  5. Michele_Laino
    • one year ago
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    since we have: \[\Large \frac{{52}}{{10}} < \frac{{54}}{{10}} < \frac{{55}}{{10}}\]

  6. anonymous
    • one year ago
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    so 5.4 is the answer

  7. Michele_Laino
    • one year ago
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    yes it is the first part of your answer, now we have to find an irrational number

  8. anonymous
    • one year ago
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    yes

  9. Michele_Laino
    • one year ago
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    an irrational number is pi=3.14159...

  10. Michele_Laino
    • one year ago
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    nevertheless 3.14159...<5.2

  11. Michele_Laino
    • one year ago
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    so we consider this number: 1.7* pi, namely: 1.7*3.14159... now, what is 1.7*3.14159..=...?

  12. anonymous
    • one year ago
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    um

  13. Michele_Laino
    • one year ago
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    namely, what is: \[\Large 1.7 \cdot \pi = ...?\]

  14. Michele_Laino
    • one year ago
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    you can use your calculator

  15. Michele_Laino
    • one year ago
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    I got this: 5.3407075111026485053864937515752... am I right?

  16. anonymous
    • one year ago
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    yes thats what i got

  17. Michele_Laino
    • one year ago
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    and that number is greater than 5.2 and less than 5.5, so it is the requested irrational number

  18. Michele_Laino
    • one year ago
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    we can rewrite it like below: \[\Large 1.7 \cdot \pi = \frac{{17\pi }}{{10}}\]

  19. Michele_Laino
    • one year ago
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    and, as you can see, its approximated value to the nearest hundredth is 5.34

  20. Michele_Laino
    • one year ago
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    and we can write this: \[\Large 5.2 < \frac{{17\pi }}{{10}} < 5.5\]

  21. anonymous
    • one year ago
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    sorry i had to go eat

  22. anonymous
    • one year ago
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    um so 17/10 is the answer for irrational

  23. Michele_Laino
    • one year ago
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    it is: \[\Large \frac{{17\pi }}{{10}}\] please study my replies here

  24. anonymous
    • one year ago
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    okay

  25. Michele_Laino
    • one year ago
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    :)

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