how to convert 3/11 into a decimal without calculator

- anonymous

how to convert 3/11 into a decimal without calculator

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- anonymous

@butterflydreamer

- anonymous

will medal

- anonymous

@midhun.madhu1987

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- UsukiDoll

wait we need to divide backwards 11 / 3

- UsukiDoll

ok that sounds better so instead of writing 3 divided by 11
we have to write 11 divided by 3 |dw:1438086137639:dw|

- anonymous

yes..

- UsukiDoll

so 11 can't divide into 3... therefore we put a 0 on the top... then the decimal point
and followed by another 0 inside the radicand (which is the number under the radical symbol )

- arindameducationusc

##### 1 Attachment

- UsukiDoll

|dw:1438086220346:dw|

- UsukiDoll

so 11 can divide into 30 at least twice
so 11 x 2 = 22 |dw:1438086248108:dw|

- UsukiDoll

since 11 can't divide 8 I have to draw another 0 making the number 80
how many times can 11 go into 80?
the closest is 7 because 11 x 7 = 77

- arindameducationusc

check this.... further @UsukiDoll can explain, Usaki is awesome.

- UsukiDoll

|dw:1438086315178:dw| then we continue this process until we hit a repeating decimal situation or can get a 0 in the remainder

- anonymous

yeah im following @arindameducationusc

- arindameducationusc

In this division it will repeat 0.272727272727......

- UsukiDoll

an example of a repeating decimal is 0.3555555555555555555555

- UsukiDoll

or what @arindameducationusc wrote.. that was funny Usaki XD

- UsukiDoll

but yes when I'm dividing this for a while I am noticing a pattern.. since I have the remainder 3 .. I have to write a 0 in the radicand and drop it down... again how many times that 11 go into 30?
2 times ..
11 x 2 = 22
then I will get an 8.
11 can't divide into 8 so I have to draw another 0
now I have 80 again
then 11 can divide into 80 at least 7 times because 11 x 7 = 77
and then
80-77 = 3 so it's a never ending repeating decimal cycle

- UsukiDoll

a line is drawn on top of the numbers to indicate that these particular numbers are going to repeat and go on and on and on and on....

- UsukiDoll

@arindameducationusc your work is correct.. :) so fast too XD

- anonymous

thanks guys @UsukiDoll

- UsukiDoll

|dw:1438086575073:dw|

- anonymous

brill explanation!

- UsukiDoll

thanks XD!

- anonymous

Lol i agree what @UsukiDoll said about @arindameducationusc but thanks to @arindameducationusc for the attachement

- UsukiDoll

my drawing was kind of horrible XD. but on my netbook it's even worse. I got no control over the touchpad.

- anonymous

dont worry pal

- anonymous

btw where did the 77 go @UsukiDoll

- UsukiDoll

oh it was squished in here.

- anonymous

dont we do 77 - 22

- UsukiDoll

|dw:1438086885416:dw|
no we don't do 77-22 at all

- anonymous

ahh dont matter thanks for the clarification

- UsukiDoll

maybe image by image will work
|dw:1438087026830:dw|

- UsukiDoll

|dw:1438087143255:dw|

- UsukiDoll

|dw:1438087206640:dw|

- anonymous

yeah thanks mate i understand it

- UsukiDoll

noticed that we have a 3 again? we know that 11 can't divide into 3, so we need to write another 0.
|dw:1438087323664:dw|
now 11 can divide 30 at least 2 times because 11 x 2 = 22
so now we subtract
30-22= 8
wait a sec we have the same pattern over and over again. STOP! We have a repeating decimal. so the final answer is 0.272727272727

- anonymous

yess!!

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