Question

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.

Answer 1

this si the last question.

Answer 2

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

Answer 3

okay

Answer 4

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

Answer 5

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

Answer 6

so 5.4 is the answer

Answer 7

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

Answer 8

yes

Answer 9

an irrational number is pi=3.14159...

Answer 10

nevertheless 3.14159...<5.2

Answer 11

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

Answer 12

um

Answer 13

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

Answer 14

you can use your calculator

Answer 15

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

Answer 16

yes thats what i got

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

sorry i had to go eat

Answer 22

um so 17/10 is the answer for irrational

Answer 23

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

Answer 24

okay

Answer 25

:)