Question
Express the following as a fraction in simplest form:
$0.\overline{24}$
$0.\overline{24}$
✓
Answer
Let $\text{x}=0. \overline{24}$
$\therefore\text{x}=0.2424\dots(1)$
$\text{100x}=24.2424\dots(2)$
On subtracting equation $(1)$ from $(2),$ we get
$\text{99x}=24$
$\Rightarrow\text{x}=\frac{8}{33}$
$\therefore0.24=\frac{\bar{8}}{33}$
$\therefore\text{x}=0.2424\dots(1)$
$\text{100x}=24.2424\dots(2)$
On subtracting equation $(1)$ from $(2),$ we get
$\text{99x}=24$
$\Rightarrow\text{x}=\frac{8}{33}$
$\therefore0.24=\frac{\bar{8}}{33}$
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 point $P$ is $25\ cm$ away from the centre of a circle and the length of tangent drawn from $P$ to the circle is $24\ cm$. Find the radius of the circle.
→In the following figure, shows a sector of a circle, centre $O,$ containing an angle $\theta^\circ.$ Prove that:
Area of the shaded region is $\frac{\text{r}^2}{2}\Big(\tan\theta-\frac{\pi\theta}{180}\Big)$
→Area of the shaded region is $\frac{\text{r}^2}{2}\Big(\tan\theta-\frac{\pi\theta}{180}\Big)$
The numerator of a fraction is $4$ less than the denominator. If the numerator is decreased by $2$ and denominator is increased by $1,$ then the denominator is eight times the numerator. Find the fraction.
→The sums of first $n$ terms of three $A.P. $ $S$ are $\mathrm{S}_1, \mathrm{~S}_2$ and $\mathrm{S}_3$. The first term of each is $5$ and their common differences are $2,4$ and $6$ respectively. Prove that $S_1+S_3=2 S_2$.
→If the points $A(-2, 1), B(a, b)$ and $C(4, -1)$ ae collinear and $a - b = 1,$ find the values of $a$ and $b.$
→Two vertices of a triangle are $(1, 2), (3, 5)$ and its centroid is at the origin. Find the coordinates of the third vertex.
→Find the lengths of the arcs cut off from a circle of radius $12\ cm$ by a chord $12\ cm$ long. Also, find the area of the minor gment. $\big[\text{Take }\pi=3.14\text{ and }\sqrt{3}=1.73.\big]$
→Prove the following trigonometric identities.
$\frac{\cos\text{A cosec A}-\sin\text{A}\sec\text{A}}{\cos\text{A}+\sin\text{A}}=\text{cosec A}-\sec\text{A}$
→$\frac{\cos\text{A cosec A}-\sin\text{A}\sec\text{A}}{\cos\text{A}+\sin\text{A}}=\text{cosec A}-\sec\text{A}$
A bucket is in the form of a frustum of a cone and holds $28.490$ litres of water. The radii of the top and bottom are $28\ cm$ and $21\ cm$ respectively. Find the height of the bucket.
→In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\sin\text{A} = \frac{2}{3}$
→$\sin\text{A} = \frac{2}{3}$