## what is .65 2/3 in fraction form?

Fractions, ratios, percentages, exponents, number patterns, word problems without variables, etc.
confused
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Joined: Sun Feb 22, 2009 10:07 pm

### what is .65 2/3 in fraction form?

what is .65 2/3 in fraction form?

stapel_eliz
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By ".65 2/3", do you mean "65 2/3%" ("sixty-five and two-thirds percent") or "0.65666666..."?

Thank you!

confused
Posts: 20
Joined: Sun Feb 22, 2009 10:07 pm

### Re: what is .65 2/3 in fraction form?

its .65666666...

DAiv
Posts: 35
Joined: Tue Dec 16, 2008 7:47 pm
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### Re: what is .65 2/3 in fraction form?

its .65666666...
We can break up the number into two parts:

$0.65 \,+\, 0.00666666...$

and in fraction form, those parts become:

$\frac{65}{100} \,+\, \frac{0.666666...}{100}$

$= \frac{65}{100} \,+\, \frac{\frac23}{100}$

Now, we need to get rid of the $\frac23$, so we multiply both fractions by $\frac33$, which will keep their denominators (bottom numbers) the same:

$= \frac{65}{100} \, \left(\frac33\right) \,+\, \frac{\frac23}{100} \, \left(\frac33\right)$

$= \frac{195}{300} \,+\, \frac2{300}$

$= \frac{197}{300}$

And as a check, we can divide 197 by 300 on a calculator to get:

$0.656666667$

... which is what we started with (with the last digit rounded up).

By ".65 2/3", do you mean "65 2/3%" ("sixty-five and two-thirds percent") or "0.65666666..."?
Incidentally, $65 \frac23 % \,=\, \frac{65 \frac23}{100} \,=\, \frac{197}{300} \,=\, 0.65666666... \,=\, 65.666666... / 100 \,=\, 65 \frac23 %$

DAiv