Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$ $125.\bar{3}$
✓
Answer
Let $\text{x}=4.\bar{7}$
$\Rightarrow\text{x}=4.77\ ...(\text{i})$ Multiplying equation $(i)$ by $10,$
$\therefore10\text{x}=47.77\ ...(\text{ii})$ Subtracting equation $(i)$ by $(ii)$
$\therefore\ 10\text{x}-\text{x}=47.77 \ ... -4.77 \ ...$
$\Rightarrow9\text{x}=43$
$\Rightarrow\text{x}=\frac{43}{9}$ Hence, $4.\bar{7}=\frac{43}{9}$
$\Rightarrow\text{x}=4.77\ ...(\text{i})$ Multiplying equation $(i)$ by $10,$
$\therefore10\text{x}=47.77\ ...(\text{ii})$ Subtracting equation $(i)$ by $(ii)$
$\therefore\ 10\text{x}-\text{x}=47.77 \ ... -4.77 \ ...$
$\Rightarrow9\text{x}=43$
$\Rightarrow\text{x}=\frac{43}{9}$ Hence, $4.\bar{7}=\frac{43}{9}$
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
How many litres of water flows out of a pipe having an area of cross section of $5 cm^2$ in $1$ minute, if the speed of water in the pipe is $30 cm / sec$ ?
→In $\triangle\text{PQR},\angle\text{A}=\angle\text{Q}$ and $\angle\text{B}=\angle\text{R}.$ Which side of should be equal to side AB of so, that the two triangles are congruent? Give reason for your answer.
→Construct the following and give justification: An equilateral triangle if its altitude is $3.2\ cm.$
→In a triangle $ABC,$ the medians $BE$ and $CF$ intersect at $G.$ Prove that $\text{ar}(\triangle\text{BCG})=\text{ar}(\text{AFGE}.)$
→Give the geometric representations of the following equations:
$a.$ On the number line.
$b.$ On the Cartesain plane.
$x = 2$
→$a.$ On the number line.
$b.$ On the Cartesain plane.
$x = 2$
Write linear equation $3 x+2 y=18$ in the form of $a x+b y+c=0$. Also write the values of $a, b$ and $c$. Are $(4,3)$ and $(1,2)$ solution of this equation?
→The following is the distribution of total household expenditure (in ₹) of manual worker in a city:
Draw a histogram and a frequency polygon representing the above data.
→→| Expenditure (in ₹): | $100-150$ | $150-200$ | $200-250$ | $250-300$ | $300-350$ | $350-400$ | $400-450$ | $450-500$ |
| No. of manual workers: | $25$ | $40$ | $33$ | $28$ | $30$ | $22$ | $16$ | $8$ |
Recall that two circles are congruent if they have a same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
Sides of a triangle are in the ratio of $12: 17: 25$ and its perimeter is $540 \ cm$. Find its area.
→