Using binomial theorem, the value of (0.999)^3 correct to 3 decim… - Vidyadip

MCQ

Using binomial theorem, the value of $(0.999)^3$ correct to $3$ decimal places is:

A
$0.999$
B
$0.998$
✓
$0.997$
D
$0.995$

✓

Answer

Correct option: C.

$0.997$

$ (0.999)^3=(1-0.001)^3 $
$ ={ }^3 C_0-{ }^3 C_1(0.001)+{ }^3 C_2(0.001)^2-{ }^3 C_3(0.001)^3 $
$ =1-0.003+3(0.000001)-(0.000000001) $
$ =0.997 $

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 "M.C.Q (1 Marks)" from Binomial Theorem→Binomial Theorem — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $x,y,z$ are in $A.P.$ and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in other $A.P.$ then . . .

If the line $x = k$ touches the circle ${x^2} + {y^2} = 9$, then the value of $k$ is

If $f(x) = \left\{ \begin{array}{l}\sin x,x \ne n\pi ,n \in Z\\\,\,\,\,\,\,0,\,\,{\rm{otherwise}}\end{array} \right.$ and $g(x) = \left\{ \begin{array}{l}{x^2} + 1,x \ne 0,\,2\\\,\,\,\,\,\,\,\,4,x = 0\\\,\,\,\,\,\,\,\,\,5,x = 2\end{array} \right.$ then $\mathop {\lim }\limits_{x \to 0} g\{ f(x)\} = $

Angle between two curves ${y^2} = 4(x + 1)$ and ${x^2} = 4(y + 1)$ is .............. $^\circ$

Which set is the subset of all given sets

The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is

Choose the correct answer. The tangent of angle between the lines whose intercepts on the axes are $a, -b$ and $b, -a,$ respectively, is

The sum of the coefficients in the expansion of ${(1 + x - 3{x^2})^{2163}}$ will be

$\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}$ is equal to

The smallest set $A$ such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$ is