Question

1.Please help what is the fraction of .666 thanks step by step please

Answer 1

Quick answer is 2/3

Answer 2

more complex answer would be to show how as the number of decimal places increases, so more sixes, then the fraction would approach 2/3.

Answer 3

go On mathway.com it really helps w/ a lot of math questions :)

Answer 4

\[x=.6666...\\
10x=6.6666...\\
9x=6\\
x=\frac{6}{9}=\frac{2}{3}\] is one method

Answer 5

How did you get the 2/3

Answer 6

forgot about that method

Answer 7

i would go with Satelites method

Answer 8

steps were
a) multiply by \(10\)
b) subtract \(x\)
c) divide by \(9\)

Answer 9

clear or you want me to do it step by step again?

Answer 10

Yes please

Answer 11

Levie wanted an explanation to getting that fraction

To convert your decimal to a fraction, you must divide 0.666 by 1, so you'll have
\[\frac{0.666}{ 1 }\] You then multiply the numerator and denominator by 10 until you eliminate any decimals...
\[\frac{0.666*1000}{1*1000}=\frac{666}{1000}\]
You can now simplify numerator and denominator by dividing it by common factors. You can divide both by 2
\[\frac{666/2}{1000/2}=\frac{333}{500}\] That is as far as you can evenly simplify it.

Answer 12

ok we call \(.6666...\) a variable \(x\) and then solve for it
first write
\[x=.6666...\]

Answer 13

then multiply it by \(10\)
on the left you get \(10x\)and on the right you move the decimal over one place and get \(6.666...\) so we have
\[10x=6.666...\]

Answer 14

then subtract \(x\) from both sides.
\(10x-x=9x\) and \(6.666...-.6666...=6\) as all the repeating decimals go
that gives
\[9x=6\]

Answer 15

finally divide by \(9\) and you get
\[x=\frac{6}{9}\] which is the same as \[x=\frac{2}{3}\]

Answer 16

btw
\[0.1111...=\frac{1}{9}\\
0.2222...=\frac{2}{9}\\
0.3333...=\frac{3}{9}\\
0.4444...=\frac{4}{9}\] etc

Answer 17

Thanks all

Answer 18

yw