Download App

Geometric Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSGeometric Progressions2 Marks
Question
Find the rational number whose decimal expansion is $0.\overline{423}.$
✓

Answer

$0.\overline{4.23}=0.4+0.0232323\ \dots$ $=0.4+0.023+0.00023+\ \dots$ $=0.4+\frac{23}{10^3}+\frac{23}{10^5}+\dots$ $=0.4+\frac{23}{10^3}\Big(1+\frac{1}{10^2}+\frac{1}{10^4}+\dots\Big)$ $=0.4+\frac{23}{1000}\Bigg(\frac{1}{1-\frac{1}{100}}\Bigg)$ $=0.4+\frac{23}{1000}\Big(\frac{100}{99}\Big)$ $=\frac{4}{10}+\frac{23}{990}$ $=\frac{360+23}{990}$ $0.\overline{423}=\frac{419}{990}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from Geometric Progressions→Geometric Progressions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Convert the complex number in the polar form: $-3$
→
Find: The $8^{th}$ term of the G.P. 0.3, 0.06, 0.012, ...
→
A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.
→
List all the element of the following sets: D = {x : x is a vowel in the word "EQUATION"};
→
If a is the G.M. of 2 and $\frac14,$ find a.
→
Show that the area of the triangle formed by the lines $y = m_1 x + c_1 , y = m_2x + c_2$ and $x = 0$ is $\frac{\left(c_{1}-c_{2}\right)^{2}}{2\left|m_{1}-m_{2}\right|}$
→
Find the multiplicative inverse of 2 - 3i.
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\sin5\text{x}}{\tan3\text{x}}$
→
Find the inverse relation R-1 in the following case:
$\text{R}=\{(\text{x, y}):\text{x},\text{ y}\in\text{N},\text{ x}+2\text{y}=8\}$
→
Prove that: $\cos\frac{7\pi}{12}+\cos\frac{\pi}{12}=\sin\frac{5\pi}{12}-\sin\frac{\pi}{12}$
→