Question 1132706


{{{sqrt(312.117 )=17.666833=17.667}}}

Decimal number is converted into binary by dividing the number successively by {{{2}}} and printing the remainder in reverse order.

Divide the number by {{{2}}}.

{{{17.667/2=8.8335}}}.....remainder {{{1}}}

{{{8.8335/2=4.41675}}}.....remainder {{{0}}}


{{{4.41675/2=2.208375}}}.....remainder {{{0}}}

{{{2.208375/2=1.1041875}}}.....remainder {{{0}}}

{{{1.1041875/2=0.55209375}}}.....remainder {{{1}}}

so far binary number is {{{10001}}}, here comes decimal point
after that you have

{{{55209375/2=276046875}}}.....remainder {{{1}}}
{{{276046875/2=1380234375}}}.....remainder {{{0}}}
{{{1380234375/2=6901171875}}}.....remainder {{{1}}}
{{{6901171875/2=34505859375}}}.....remainder {{{0}}}
{{{34505859375/2=17252929687}}}.....remainder {{{1}}}
{{{17252929687/2=8626464843}}}.....remainder {{{1}}}
{{{8626464843/2=4313232421}}}.....remainder {{{0}}}
{{{4313232421/2=215661621}}}.....remainder {{{0}}}
{{{215661621/2=107830810}}}.....remainder {{{0}}}
{{{107830810/2= 53915405}}}.....remainder {{{1}}}
{{{53915405/2=26957702}}}.....remainder {{{1}}}
{{{26957702/2=13478851}}}.....remainder {{{0}}}
{{{13478851/2=6739425}}}.....remainder {{{1}}}
{{{6739425/2=3369712}}}.....remainder {{{0}}}
{{{3369712/2=1684856}}}.....remainder {{{1}}}
:
so on up to reminder is {{{0}}}

Binary number:{{{ 10001.101011000110101}}}

when I convert it to decimal, I got

{{{17.673492431640625}}} which is approximately {{{17.667}}}