You know that $\frac{1}{7}=0 . \overline{142857}$. Can you predict what the decimal expansions of $\frac{2 }{7},\, \frac{3}{7}$, $\frac{4}{7},\, \frac{5}{7}, \,\frac{6}{7}$ are, without actually doing the long division ? If so, how ?
You know that $\frac{1}{7}=0 . \overline{142857}$. Can you predict what the decimal expansions of $\frac{2 }{7},\, \frac{3}{7}$, $\frac{4}{7},\, \frac{5}{7}, \,\frac{6}{7}$ are, without actually doing the long division ? If so, how ?
We are given that $\frac{1}{7}=0 . \overline{142857}$
$\frac{2}{7}=2 \times \frac{1}{7}=2 \times(0 . \overline{142857})=0 . \overline{285714}$
$\frac{3}{7}=3 \times \frac{1}{7}=3 \times(0 . \overline{142857})=0.4 \overline{28571}$
$\frac{4}{7}=4 \times \frac{1}{7}=4 \times(0 . \overline{142857})=0 . \overline{571428}$
$\frac{5}{7}=5 \times \frac{1}{7}=5 \times(0 . \overline{142857})=0 . \overline{714285}$
$\frac{6}{7}=6 \times \frac{1}{7}=6 \times(0 . \overline{142857})=0 . \overline{857142}$
Thus, without actually doing the long division we can predict the decimal expansions of the above given rational numbers.
Similar Questions
Rationalise the denominators of the following :
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$
Rationalise the denominators of the following :
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$
Find an irrational number between $\frac {1}{7}$ and $\frac {2}{7}$
Find an irrational number between $\frac {1}{7}$ and $\frac {2}{7}$
Show that $1.272727 \ldots=1 . \overline{27}$ . can be expressed in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Show that $1.272727 \ldots=1 . \overline{27}$ . can be expressed in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.
Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.
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 $q \ne 0$.