Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$0.\bar{4}$
✓
Answer
Let$\text{x}=0.\bar4$
Now,$\text{x}=0.\bar4=0.444\ ...(\text{i})$
Multiplying both sides of equation (i) by 10, we get,$10\text{x}=4.444\ ...(\text{ii}) $
Subtracting equation (i) by (ii)$\therefore\ 10\text{x}-\text{x}=4.444\ ...-\ 0.444\ ...$
$\Rightarrow9\text{x}=4$
$\Rightarrow\text{x}=\frac{4}{9}$
Hence, $0.\bar{4}=\frac{4}{9}$
Now,$\text{x}=0.\bar4=0.444\ ...(\text{i})$
Multiplying both sides of equation (i) by 10, we get,$10\text{x}=4.444\ ...(\text{ii}) $
Subtracting equation (i) by (ii)$\therefore\ 10\text{x}-\text{x}=4.444\ ...-\ 0.444\ ...$
$\Rightarrow9\text{x}=4$
$\Rightarrow\text{x}=\frac{4}{9}$
Hence, $0.\bar{4}=\frac{4}{9}$
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
If $a+b+c=9$ and $a^2+b^2+c^2=35$, find the value of $\left(a^3+b^3+c^3-3 a b c\right)$.
→What are:
- Primary data,
- Secondary data?
Write two solutions for the following equations:$\frac{2}{3}\text{x} - \text{y} = 4$
→There are instructions written near the arrows in the following diagram. From this information form suitable equations and write in the boxes indicated by arrows. Select any two equations from these boxes and find their solutions. Also verify the solutions. By taking one pair of equations at a time, how many pairs can be formed ? Discuss the solutions for these pairs.
Find the value of x for which the angles (2x - 5)º and (x - 10)º are the complementary angle.
In the adjoining figure, CE || AD and CF || BA. Prove that $\text{ar}(\triangle\text{CBG})=\text{ar}(\triangle\text{AFG}).$
→Factorize the following expressions:
$8x^2y^3- x^5$
→$8x^2y^3- x^5$
Solve the following sets of simultaneous equations : x + y = 4 ; 2x – 5y = 1
Evaluate:$\Big(\frac{1}{2}\Big)^3+\Big(\frac{1}{3}\Big)^3=\Big(\frac{5}{6}\Big)^3$
→In each of the following determine rational numbers a and b:$\frac{4+3\sqrt5}{4-3\sqrt5}=\text{a}+\text{b}\sqrt{5}$
→