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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

this si the last question.

2. Michele_Laino

we can write this: $\Large 5.2 = \frac{{52}}{{10}},\quad 5.5 = \frac{{55}}{{10}}$

3. anonymous

okay

4. Michele_Laino

so a rational number between 5.2 and 5.5 can be: $\Large \frac{{54}}{{10}} = 5.4$

5. Michele_Laino

since we have: $\Large \frac{{52}}{{10}} < \frac{{54}}{{10}} < \frac{{55}}{{10}}$

6. anonymous

so 5.4 is the answer

7. Michele_Laino

yes it is the first part of your answer, now we have to find an irrational number

8. anonymous

yes

9. Michele_Laino

an irrational number is pi=3.14159...

10. Michele_Laino

nevertheless 3.14159...<5.2

11. Michele_Laino

so we consider this number: 1.7* pi, namely: 1.7*3.14159... now, what is 1.7*3.14159..=...?

12. anonymous

um

13. Michele_Laino

namely, what is: $\Large 1.7 \cdot \pi = ...?$

14. Michele_Laino

you can use your calculator

15. Michele_Laino

I got this: 5.3407075111026485053864937515752... am I right?

16. anonymous

yes thats what i got

17. Michele_Laino

and that number is greater than 5.2 and less than 5.5, so it is the requested irrational number

18. Michele_Laino

we can rewrite it like below: $\Large 1.7 \cdot \pi = \frac{{17\pi }}{{10}}$

19. Michele_Laino

and, as you can see, its approximated value to the nearest hundredth is 5.34

20. Michele_Laino

and we can write this: $\Large 5.2 < \frac{{17\pi }}{{10}} < 5.5$

21. anonymous

sorry i had to go eat

22. anonymous

um so 17/10 is the answer for irrational

23. Michele_Laino

it is: $\Large \frac{{17\pi }}{{10}}$ please study my replies here

24. anonymous

okay

25. Michele_Laino

:)

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