MHT CET · Maths · Sequences and Series
The rational form of a number \(1 \cdot \overline{41}\) is
- A \(\frac{154}{99}\)
- B \(\frac{55}{99}\)
- C \(\frac{140}{99}\)
- D \(\frac{41}{99}\)
Answer & Solution
Correct Answer
(C) \(\frac{140}{99}\)
Step-by-step Solution
Detailed explanation
The rational form of a number \(1.41\) is \(\frac{140}{99}\).
Let \(x=1.414141 \quad\)...(i) \(100 x=141.414141 \quad\)...(ii)
Subtract Eq. (i) from Eq. (ii), we get
\(99 x=140\)
\(x=\frac{140}{99}\) \(\therefore 1 . \overline{41}=\frac{140}{99}\)
Let \(x=1.414141 \quad\)...(i) \(100 x=141.414141 \quad\)...(ii)
Subtract Eq. (i) from Eq. (ii), we get
\(99 x=140\)
\(x=\frac{140}{99}\) \(\therefore 1 . \overline{41}=\frac{140}{99}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int \frac{\sec ^8 x}{\operatorname{cosec} x} d x=\)MHT CET 2021 Hard
- For every value of \(x\), the function \(f(x)=\frac{1}{a^{x}}, a>0\) isMHT CET 2020 Easy
- The circles \(x^2+y^2+2 \mathrm{a} x+\mathrm{c}=0\) and \(x^2+y^2+2 \mathrm{~b} y+\mathrm{c}=0\) touch each other externally, ifMHT CET 2023 Easy
- The integrating factor of differential equation \(\left(1+y+x^{2} y\right) d x+\left(x+x^{3}\right) d y=0\) isMHT CET 2020 Medium
- \(\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{~d} x=\)MHT CET 2024 Medium
- The value of is ________MHT CET 2019 Hard
More PYQs from MHT CET
- A moving body with mass ' \(\mathrm{m}_1\) ' strikes a stationary mass ' \(m_2\) '. What should be the ratio \(\frac{m_1}{m_2}\) so as to decrease the velocity of first by (1.5) times the velocity after the collision?MHT CET 2024 Hard
- In brood parasitism _________.MHT CET 2021 Easy
- If \(f(x)=\frac{e^{x^2}-\cos x}{x^2}\) if \(x \neq 0\) is continuous at \(x=0\), then \(f(0)=\).MHT CET 2022 Medium
- Which among following statement is NOT true for neoprene?MHT CET 2021 Easy
- The integral \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x \mathrm{~d} x\) is equal toMHT CET 2023 Hard
- Which among the following solids is a non-polar solid?MHT CET 2016 Easy