anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
this si the last question.
Michele_Laino
  • Michele_Laino
we can write this: \[\Large 5.2 = \frac{{52}}{{10}},\quad 5.5 = \frac{{55}}{{10}}\]
anonymous
  • anonymous
okay

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Michele_Laino
  • Michele_Laino
so a rational number between 5.2 and 5.5 can be: \[\Large \frac{{54}}{{10}} = 5.4\]
Michele_Laino
  • Michele_Laino
since we have: \[\Large \frac{{52}}{{10}} < \frac{{54}}{{10}} < \frac{{55}}{{10}}\]
anonymous
  • anonymous
so 5.4 is the answer
Michele_Laino
  • Michele_Laino
yes it is the first part of your answer, now we have to find an irrational number
anonymous
  • anonymous
yes
Michele_Laino
  • Michele_Laino
an irrational number is pi=3.14159...
Michele_Laino
  • Michele_Laino
nevertheless 3.14159...<5.2
Michele_Laino
  • Michele_Laino
so we consider this number: 1.7* pi, namely: 1.7*3.14159... now, what is 1.7*3.14159..=...?
anonymous
  • anonymous
um
Michele_Laino
  • Michele_Laino
namely, what is: \[\Large 1.7 \cdot \pi = ...?\]
Michele_Laino
  • Michele_Laino
you can use your calculator
Michele_Laino
  • Michele_Laino
I got this: 5.3407075111026485053864937515752... am I right?
anonymous
  • anonymous
yes thats what i got
Michele_Laino
  • Michele_Laino
and that number is greater than 5.2 and less than 5.5, so it is the requested irrational number
Michele_Laino
  • Michele_Laino
we can rewrite it like below: \[\Large 1.7 \cdot \pi = \frac{{17\pi }}{{10}}\]
Michele_Laino
  • Michele_Laino
and, as you can see, its approximated value to the nearest hundredth is 5.34
Michele_Laino
  • Michele_Laino
and we can write this: \[\Large 5.2 < \frac{{17\pi }}{{10}} < 5.5\]
anonymous
  • anonymous
sorry i had to go eat
anonymous
  • anonymous
um so 17/10 is the answer for irrational
Michele_Laino
  • Michele_Laino
it is: \[\Large \frac{{17\pi }}{{10}}\] please study my replies here
anonymous
  • anonymous
okay
Michele_Laino
  • Michele_Laino
:)

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