Tag: decimal fractions

$0.585 = 0.5+0.08+0.005 = \dfrac{5}{10} + \dfrac{8}{100} + \dfrac{5}{1000}$
$0.585 = \dfrac{585}{1000}$

$\dfrac {2008}{1000} = \dfrac {1004}{500}$

$\dfrac {2}{10}\times \dfrac {2}{100} \times \dfrac {2}{1000}$

$\displaystyle 2.\overline{8768}=2+0.\overline{8768}$
= $\displaystyle 2+\frac{8768-8}{9990}=2+\frac{8760}{9990}$
= $\displaystyle 2+\frac{292}{333}=2\frac{292}{333}$

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify:
$2.45 = 2\cfrac{45}{100} = 2\cfrac{9}{20}$    ...Mixed fraction

$53.234 = \dfrac {53234}{1000} = \dfrac {53234}{10^{3}}$
Denominator is $1000$.
Therefore, $C$ is the correct answer.

$Let\quad x=0.212121...\ 100x=21.212121....\ 100x-x=21\ 99x=21\ x=\frac { 21 }{ 99 } =\frac { 7 }{ 33 } $

Zeroes placed between other digits are always significant.
$\therefore  3.005$ has $4$ significant digits.

$5.16\times 10^8$
There are $3$ significant figures. When a number is  written in scientific notation, only significant figures are placed into the numerical portion.

All zeroes which are both to the right of the decimal point and to the right of all non-zero significant digits are themselves significant.
$\therefore  16.000$ has $5$ significant digits