Answer:
7/18 8/18 9/18 10/18 11/18
Step-by-step explanation:
1/3×6=6/18 2/3×6=12/18
ans 7/18 8/18 9/18 10/18 11/18
[tex]\large\underline\color{grey}{\sf{Solution\: : - }}[/tex]
To find Rational numbers between any two numbers a and b :
Multiply same number with numerator and denominator :
[tex]\dfrac{1}{3}\times\dfrac{6}{6}[/tex] : [tex]\dfrac{6}{18}[/tex]
[tex]\dfrac{2}{3}\times\dfrac{6}{6} : \dfrac{12}{18}[/tex]
Now , Write any five rational numbers in between[tex]\dfrac{6}{18}[/tex]and [tex]\dfrac{12}{18}[/tex]
The Rational numbers between[tex]\dfrac{1}{3}[/tex] and [tex]\dfrac{2}{3}[/tex] are :
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\dfrac{13}{18}[/tex], [tex]\dfrac{14}{18}[/tex],[tex]\dfrac{15}{18}[/tex],[tex]\dfrac{16}{18}[/tex],[tex]\dfrac{17}{18}[/tex]
Here , are the rational numbers .
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\color{black}\boxed{\dfrac{a + b}{2}}[/tex]
So, the rational number between [tex]\dfrac{1}{3}, \dfrac{2}{3}[/tex] is
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{1/3 + 2/3}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{1 + 2/ 3}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{\cancel3/\cancel3}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{1/1}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex][tex]\color{black}\boxed{\dfrac{1}{2}}[/tex]
Here, [tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\dfrac{1}{3}[/tex] = 0.333 and
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\dfrac{2}{3}[/tex] = 0.6666
We know that non terminating and non recurring decimal is irrational number .
Here 0.4413691 is non terminating and non recurring decimal which lies between 0.333 ..and 0.6666..
So ,the irrational number between 0.333 and 0.6666 is 0.4413691.
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Answers & Comments
Verified answer
Answer:
7/18 8/18 9/18 10/18 11/18
Step-by-step explanation:
1/3×6=6/18 2/3×6=12/18
ans 7/18 8/18 9/18 10/18 11/18
[tex]\large\underline\color{grey}{\sf{Solution\: : - }}[/tex]
To find Rational numbers between any two numbers a and b :
Multiply same number with numerator and denominator :
[tex]\dfrac{1}{3}\times\dfrac{6}{6}[/tex] : [tex]\dfrac{6}{18}[/tex]
[tex]\dfrac{2}{3}\times\dfrac{6}{6} : \dfrac{12}{18}[/tex]
Now , Write any five rational numbers in between[tex]\dfrac{6}{18}[/tex]and [tex]\dfrac{12}{18}[/tex]
The Rational numbers between[tex]\dfrac{1}{3}[/tex] and [tex]\dfrac{2}{3}[/tex] are :
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\dfrac{13}{18}[/tex], [tex]\dfrac{14}{18}[/tex],[tex]\dfrac{15}{18}[/tex],[tex]\dfrac{16}{18}[/tex],[tex]\dfrac{17}{18}[/tex]
Here , are the rational numbers .
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To find Irrational number between two numbers a and b
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\color{black}\boxed{\dfrac{a + b}{2}}[/tex]
So, the rational number between [tex]\dfrac{1}{3}, \dfrac{2}{3}[/tex] is
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{1/3 + 2/3}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{1 + 2/ 3}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{\cancel3/\cancel3}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex] [tex]\dfrac{1/1}{2}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\hookrightarrow[/tex][tex]\color{black}\boxed{\dfrac{1}{2}}[/tex]
Here, [tex]\:\:\:\:\:\:\:\:\:\:[/tex][tex]\dfrac{1}{3}[/tex] = 0.333 and
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\dfrac{2}{3}[/tex] = 0.6666
We know that non terminating and non recurring decimal is irrational number .
Here 0.4413691 is non terminating and non recurring decimal which lies between 0.333 ..and 0.6666..
So ,the irrational number between 0.333 and 0.6666 is 0.4413691.