Given:
The values are [tex]a=0.\overline{6},b=0.75[/tex].
To find:
The values of [tex]ab[/tex] and [tex]\dfrac{a}{b}[/tex].
Solution:
We have,
[tex]a=0.\overline{6}[/tex]
[tex]a=0.666...[/tex] ...(i)
Multiply both sides by 10.
[tex]10a=6.666...[/tex] ...(ii)
Subtracting (i) from (ii), we get
[tex]10a-a=6.666...-0.666...[/tex]
[tex]9a=6[/tex]
[tex]a=\dfrac{6}{9}[/tex]
[tex]a=\dfrac{2}{3}[/tex]
And,
[tex]b=0.75[/tex]
[tex]b=\dfrac{75}{100}[/tex]
[tex]b=\dfrac{3}{4}[/tex]
Now, the product of a and b is:
[tex]ab=\dfrac{2}{3}\times \dfrac{3}{4}[/tex]
[tex]ab=\dfrac{1}{2}[/tex]
The quotient of a and b is:
[tex]\dfrac{a}{b}=\dfrac{\dfrac{2}{3}}{\dfrac{3}{4}}[/tex]
[tex]\dfrac{a}{b}=\dfrac{2}{3}\times \dfrac{4}{3}[/tex]
[tex]\dfrac{a}{b}=\dfrac{8}{9}[/tex]
Therefore, the required values are [tex]ab=\dfrac{1}{2}[/tex] and [tex]\dfrac{a}{b}=\dfrac{8}{9}[/tex].
