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anonymous
 one year ago
a rational number and an irrational number that are between 7.7 and 7.9. Include the decimal approximation of the irrational number to the nearest hundredth.
anonymous
 one year ago
a rational number and an irrational number that are between 7.7 and 7.9. Include the decimal approximation of the irrational number to the nearest hundredth.

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Do you know what rational and irrational numbers are/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its an essay question

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0rational numbers: \( \color{black}{{\bf ...}~~4,~~3,~~2,~~1,~~~~0,~~~~1,~~~~2,~~~~3,~~~~4}\) Also it can be a fraction \( \color{black}{3/5,~~~1/9,~~~~10/7,~~~~~3/9,~~~~1000/81}\) (and so on many other examples...) Also it can be a terminating decimal, or a repeating decimal (because they are technically fractions)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0if you see: Negative or positive,  number or fraction, or a decimal, (decimal which terminanting or repeating, BUT NOT some decimal without a pattern) then what you see is a rational number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find a rational number and an irrational number that are between 7.7 and 7.9. Include the decimal approximation of the irrational number to the nearest hundredth.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Also \(\sqrt{4}\) is a rational number because, really \(\sqrt{4}=2\) and 2 is rational. And any root that simplifies to a rational is a rational number. (this is all for rational numbers)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0I am giving you the definitions neccesary.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Now and irrational numbers Roots: like \(\sqrt{3}\) , \(\sqrt[6]{16}\), \(\sqrt{98}\) and other roots that don't simplify to a rational number. Also, logarithms if they don't simplify to rational number. Like \(\ln(2),~~\log_{3}(4),~~~\log_{18}(71)\) and others Also, special constant like \( \color{black}{\psi,~e,~\pi~...}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0irrational number is also something like \(4{\bf .}2946188294621536724111...\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0where the decomal is not repeating or terminating

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Ok, got the definitions of rtional and irrational numbers?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0one more, to the definition or RATIONAL number. if your decimal is finite, like 3.4 2.625 1.88 7.59 then the number is rational

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0ok, I will give you an example of how to do you problem if I have 4.2 and 4.4 and you will then do it with your numbers.....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0A rational number between 4.2 and 4.4 can for example be any decimal that is greater than 4.2 and less than 4.4 For example 4.3  An irrational number can be a square root that is less than 4.2 and greater than 4.3 For example \(4.2^2=17.64\) \(4.4^2=19.36\) So it can be a square root of any number between 17.64 and 19.36 like \(\sqrt{18}\) Check √18 = 4.242640687 (via calculator) So, now round that to nearest hunderedth √18 ≈ 4.24 (you round it down, because after a 4 is a 2 and 2 is rounded down, not up) so you found your irrational number.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0correction: A rational number between 4.2 and 4.4 can for example be any \(\color{red}{\rm finite}\) decimal that is greater than 4.2 and less than 4.4

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0(take your time)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so a rational number between 7.7 and 7.9 can be 7.756784535583495...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0ok, yes.... can you tell me how you got this number tho'?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.07.756784535583495... is irrational, no?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thought that irrational was terminating not repeating

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thought that rational was repeating

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Rational number decimals: Terminating: (like 1.\(\color{red}{34}\)3434343434 .... ) Repeating: (like 2.\(\color{red}{6}\)666666.... ) Also simple decimals that don't go on forever like: \(2.457\) \(0.5\) \(4.21\) \(43.873\) \(92.555\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0An irrational decimal is a decimal that is NOT terminating and NOT repeating. In other words, it goes forver, and doesn't have any pattern to it what so ever.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Can you tell me a rational RATIONAL number that is between \(7.7\) and \(7.8\)? (just give me a simple decimal)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so pi is irrational 3.1415926535.....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Yes, \(\pi\) (and e, if you heard of it) are definitely irrational

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0also \(\psi\) (infinite series of fibonacci reciprocals)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, 7.725 can be a rational number between 7.7 and 7.9 Nice!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Now, how about an IRRATIONAL number between 7.7 and 7.9? (remember how I found an IRRATIONAL number between 4.2 and 4.4 ?)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.07.7*7.7=59.29 7.9*7.9=62.41 \[\sqrt{60}\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, now, (using a calculator), calculate \(\sqrt{60}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you can use this site: wolframalpha.com

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0enter there "square root of 60" and it will give you the answer

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0it will simplfy it for you under "Result" but, you need the "Decimal Approximation" that it will give.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Or google can do it for you, as well: https://www.google.com/search?site=&source=hp&q=square+root+of+60&oq=square+root+of+60&gs_l=hp.3..19j0l10.1111.4707.0.5000.22.15.0.2.2.0.923.2182.1j4j0j2j61.8.0....0...1c.1.64.hp..13.9.1262.0.wj4VxQsctJM

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0so, \(\sqrt{60}=?\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes that is the exact result, and the "DECIMAL APPROXIMATION" 9what we need) is \(\sqrt{60} \approx 7.745966692....\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0now round that to nearest hunderedth and you get?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you are done i guess. you found rational and irrational numbers as needed;)
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