Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.
Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.
$\frac{5}{7}$ $=0 . \overline{714285}$
$\frac{9}{11}$ $=0 . \overline{81}$
As there are an infinite number of irrational numbers between $0 . \overline{714285}$ and $0 . \overline{81}$, any three of them can be :
$0.73073007300073000073 \ldots$
$0.75075007500075000075 \ldots $
$0 .79079007900079000079 \ldots$
Similar Questions
Simplify the following expressions :
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$
Simplify the following expressions :
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$
Is zero a rational number ? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$ ?
Is zero a rational number ? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$ ?
Write the following in decimal form and say what kind of decimal expansion each has :
$(i)$ $\frac{36}{100}$
$(ii)$ $\frac{1}{11}$
$(iii)$ $4 \frac{1}{8}$
$(iv)$ $\frac{3}{13}$
$(v)$ $\frac{2}{11}$
$(vi)$ $\frac{329}{400}$
Write the following in decimal form and say what kind of decimal expansion each has :
$(i)$ $\frac{36}{100}$
$(ii)$ $\frac{1}{11}$
$(iii)$ $4 \frac{1}{8}$
$(iv)$ $\frac{3}{13}$
$(v)$ $\frac{2}{11}$
$(vi)$ $\frac{329}{400}$
Rationalise the denominator of $\frac{1}{\sqrt{2}}$.
Rationalise the denominator of $\frac{1}{\sqrt{2}}$.
Show that $3.142678$ is a rational number. In other words, express $3.142678$ in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Show that $3.142678$ is a rational number. In other words, express $3.142678$ in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.