Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.
Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.
We can magnify an interval endlessly using successive magnification.
To visualize $4 . \overline{26}$ or $4.2626 \ldots$ on the number line up to $4$ decimal places, we use the following steps.
$I$. The number $4.2626 \ldots$ lies between $4$ and $5 .$ Divide the interval $[4,\,5]$ in $10$ smaller parts :
$II.$ Obviously, the number $4.2626 \ldots$ lies between $4.2$ and $4.3 .$ We magnify the interval $[4.2,\,4.3]$.
$III.$ Next, we magnify the interval $[4.26, \,4.27]$ :
$IV.$ Finally magnify the interval $[4.262,\,4.263]$ :
In Fig. $(iv)$, we can easily observe the number $4.2626 \ldots$ or $4 . \overline{26}$.
Similar Questions
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?
Look at several examples of rational numbers in the form $\frac{p}{q}(q \neq 0),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy ?
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 :
$(i)$ $(5+\sqrt{7})(2+\sqrt{5})$
$(ii)$ $(5+\sqrt{5})(5-\sqrt{5})$
$(iii)$ $(\sqrt{3}+\sqrt{7})^{2}$
$(iv)$ $(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})$
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 :
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
Visualize the representation of $5.3 \overline{7}$. on the number line upto $5$ decimal places, that is, up to $5.37777$.
Visualize the representation of $5.3 \overline{7}$. on the number line upto $5$ decimal places, that is, up to $5.37777$.