Question

Can someone walk through an equation with me? i'll give a medal

Answer 1

Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational. (2 points)

Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Answer 2

what's the definition of a rational number?

Answer 3

a rational number can be written as a fraction of two integers

Answer 4

right, so what fraction could represent 9?

Answer 5

um im not sure what you mean by that can you explain sorry

Answer 6

Could be 9.6 or
96/10

Answer 7

exactly, i was leading you to that but you already got there. So that's A. What's the definition of an irrational number?

Answer 8

oh, wait i thought you replied with that.... 9/1 is equal to 9, 90/10 is equal to 9

Answer 9

sorry i have a question about the first one how do we know if it's 9.6 or 96/10?

Answer 10

imagine 9 as a fraction, it's 9/1
if you multiply both sides by 10 you get 90/10
same thing with 9.6
9.6/1 *10/10 = 96/10

Answer 11

so by multiplying 9.6/1 and 10/10 you get 96/10?

Answer 12

when multiplying fractions you multiply the numerators and denominators separately, so what you get is (9.6*10)/(1*10)

Answer 13

oh okay

Answer 14

so you need a rational number between 9.5 and 9.7, 9.6 fits...
now we need to make it a fraction
9.6/1 * 10/10 = 96/10

Answer 15

because for your purposes you can't have a decimal value in a fraction

Answer 16

so how do we find the rational number

Answer 17

I guess the second part could be √93
Is irracional because is an inexact root

Answer 18

@isaidavila while your answers are appreciated it would be much more helpful if you explained to @ogjb_ how you approached and answered the problem

Answer 19

Using calculador is the only way

Answer 20

not really, 9*9 = 81
10* 10 = 100
so we're looking for the root of a number between 81 and 100

Answer 21

I never thought of it that way

Answer 22

so what is the summary of part a ?

Answer 23

9.6 is equivalent to 96/10 yes? and 9.6 is rational, therefore 96/10 is a rational number between 9.6 and 9.7

Answer 24

between 9.5 and 9.7

Answer 25

oh okay

Answer 26

for B start with the number 9 represented as a fraction with denominator 7
(9*7)/7 = 63/7

Answer 27

.5 is a little less than 4/7 (because half of 7 is 3.5) therefore
63/7 + 4/7 is between 9.5 and 9.7 and most definitely irrational

Answer 28

what is the summary of part b?

Answer 29

sorry im also taking notes

Answer 30

dude i'm in an algorithms class right now, this class is so boring
but for B we've decided to represent the irrational as a multiple of 1/7
we know 63/7 = 9 and that 4/7 is slightly greater than .5
therefore 63/7 + 4/7 is a little greater than 9.5

Answer 31

wow how do you even manage like fr

Answer 32

oh and thank you so much for your help and support i just really suck at math and you really helped me today but i hope you dont mind me asking you to help me with another question

Answer 33

no problem, but I think the site mods want you to put it in another thread

Answer 34

ok
just a sec

Answer 35

tag me in it so i can find it

Answer 36

ok

Answer 37

sorry not trying to take a long time im just trying to take notes