Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
$0.\overline{47}$
$0.\overline{47}$
✓
Answer
$0.\overline{47}=0.4777...$
Let $\text{x}=0.4777 \ ...\text{(i)}$
$10\text{x}=4.777$
$100\text{x}=47.777 \ ...(\text{ii})$
$(ii) - (i)$ gives
$99\text{x}=43$
$\text{x}=\frac{43}{99}$
Let $\text{x}=0.4777 \ ...\text{(i)}$
$10\text{x}=4.777$
$100\text{x}=47.777 \ ...(\text{ii})$
$(ii) - (i)$ gives
$99\text{x}=43$
$\text{x}=\frac{43}{99}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A dome of a building is in the form of a hemisphere. From inside, it was white$-$washed at the cost of $Rs. 4989.60$. If the cost of white$-$washing is $Rs. 20$ per square metre. Find the
$i.$ inside surface area of the dome.
$ii.$ Volume of the air inside the dome.
→$i.$ inside surface area of the dome.
$ii.$ Volume of the air inside the dome.
For the polynomial $\frac{\text{x}^3+2\text{x}+1}{5}-\frac{7}{2}\text{x}^2-\text{x}^6,$ write.
$i.$ The degree of the polynomial.
$ii.$ The coefficient of $x^3.$
$iii.$ The coefficient of $x^{6.}$
$iv.$ The constant term.
→$i.$ The degree of the polynomial.
$ii.$ The coefficient of $x^3.$
$iii.$ The coefficient of $x^{6.}$
$iv.$ The constant term.
$AB$ is a line segment and $P$ is its mid$-$point. $D $and $E$ are points on the same side of $AB$ such that $\angle BAD = \angle ABE$ and $\angle EPA = \angle DPB.$
Show that:
$i. \triangle DAP \cong \triangle EBP$
$ii. AD = BE$
→Show that:
$i. \triangle DAP \cong \triangle EBP$
$ii. AD = BE$
If the mean of five observations $x, x + 2, x + 4, x + 6, x + 8$ is $13$, find the value of x and hence find the mean of the last three obervations.
→Find the length of $13.2\ kg$ of copper wire of diameter 4mm, when $1$ cubic centimetre of copper weighs $8.4g.$
→Factorize:
$a^2 x^2+\left(a x^2+1\right) x+a$
→$a^2 x^2+\left(a x^2+1\right) x+a$
If $\sqrt{2}=1.414,\ \sqrt{3}=1.732$ then find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$
→From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are $14 \ cm, 10 \ cm$ and $6 \ cm.$ Find the area of the triangle.
→Show that $(p-1)$ is a factor of $\left(p^{10}-1\right)$ and also of $\left(p^{11}-1\right)$.
→An angle is equal to five times its complement. Determine its measure.