Question

What 1/7 with binary. Explian.tku.

Answer 1

binary fractions eh .... id have to read up on it

Answer 2

that's a new one

Answer 3

pretty sure i'm gonna pass on that

Answer 4

there is an algorithm for this which i just looked up a week ago. but the idea is this. base two fractions look like
\[\sum \frac{a_k}{2^k}\] where
\[a_k=0,1\]

Answer 5

so for example for 1/7, the largest "binary fraction" less than 1/7 is 1/8, so we are going to start with .001
meaning no 1/2,no 1/4, 1 1/8

Answer 6

1/7=0,1428571429 in decimal

Answer 7

then subtract and repeat.
\[\frac{1}{7}-\frac{1}{8}=\frac{1}{56}\] so then next one will be
.00101
meaning no 1/16 and 1 1/64

lather, rinse, repeat

Answer 8

the website I reviewed says to take the decimal and multiply it by 2 and take the integer value of it:

1/7 = 7|1 = .1428 ...

Answer 9

@amistre share the site if you would.

Answer 10

0,1428571429*2=0,2857142857
0,2857142857*2=0,5714285714
0,5714285714*2=1,1428571429
0,1428571429*2=0,2857142857
0,2857142857*2=0,5714285714
0,5714285714*2=1,1428571429
...
so in binary 1/7 looks like = 0.001001001001001001...

Answer 11

thanks makes it look much easier than the site a saw!

Answer 12

wonder why my beginning was wrong though...

\[\frac{1}{7}-\frac{1}{8}=\frac{1}{56}\] so why don't we have anything in the
\[\frac{1}{64}\] place???

Answer 13

oh because i am an idiot that's why

Answer 14

1/64 = .000001

Answer 15

i tried coping it and on a different terminal that went haywire :)

Answer 16

let's check:
\[\sum\frac{1}{8^k}=\frac{1}{1-\frac{1}{8}}=\frac{8}{7}\] subtract 1, get \[\frac{1}{7}\] fine

Answer 17

pretty much it said; take the decimal form, multiply it by 2, and shave off the integer; move the decimal over and repeat

Answer 18

right.
and the answer is
\[.001001001001...=\sum_{k=1}^{\infty}\frac{1}{8^k}\] which checks

Answer 19

.0625 for instance would amount to:

2(.0625) = 0.1250 = 0
2(.625) = 1.25 = 1
2(.25) = 0.5 = 0
2(.5) = 1.0 = 1

.0101 perhaps?

Answer 20

no you made a mistake i think

Answer 21

its quite possible I did :)

Answer 22

well first of all .0625 =1/16 right?

Answer 23

yes

Answer 24

so it should be .0001

Answer 25

second step you multiplied by 10!

Answer 26

just going off my interp of the website :) ill have to review it again

Answer 27

http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm

Answer 28

no i maean in your computation above
look at step 2

Answer 29

i misread the instructions :) i thought you moved the decimal over each time, but you actually just chop of the integer and work the new stuff

2(.0625) = 0.1250 = 0
2(.125) = 0.250 = 0
2(.25) = 0.5 = 0
2(.5) = 1.0 = 1

.0001

Answer 30

that is it! but since 16 is a power of 2 that one was easy

Answer 31

i like easy for testing ;)

Answer 32

look what you did. you multiplied by 16, got 1 and said "oh it is 1/16=.0001

Answer 33

:)

Answer 34

2(1/7) = 2/7 < 1 = 0
2(2/7) = 4/7 < 1 = 0
2(4/7) = 8/7 > 1 = 1 ; 1' 1/7
2(1/7) = 2/7 < 1 = 0
.......

.001001001...