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# 3 times what equals 10? Don't say 3.3333333333333333 cause 3*3.3333333333333333=9.9999999999999999

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3 times what equals 10? Don't say 3.3333333333333333 cause 3*3.3333333333333333=9.9999999999999999

Dec 11, 2014

#1
+114442
+8

OK....how about (3 + 1/3)  ???

Dec 11, 2014

#1
+114442
+8

OK....how about (3 + 1/3)  ???

CPhill Dec 11, 2014
#2
+270
+5

3.333333333 has no end.

For example,

$$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...$$

If you add 1/2 that is half to previous number and continue it,

you will see that the sum of those are going closer and closer to 1.

By common sense, they will never reach 1.

But,

$$S_n = \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2^n}$$

If I multiply this by 2, then we can see it equals to $$S_n$$.

$$2S_n=\frac{2}{2}+\frac{2}{4}+\frac{2}{8}+...+\frac{2}{2^n} =1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{2}{2^n^-^1} =1+S_n-\frac{1}{2^n}$$

If we subtract $$S_n$$ from both sides,

$$s_n = 1 - \frac{1}{2^n}$$

As n is infinity, $$S_n = 1.$$

I think this proof apply to your question too.

As you said 3.33333+3.33333+3.33333 = 9.99999

But 3.333...+3.333...+3.333...=1

Hope it helped!

Dec 11, 2014
#3
+1036
0

Ok flflvm97, What formula did you use for this? Base X-9 ?

But 3.333...+3.333...+3.333...=1

$$S_n = \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2^n}$$

If I multiply this by 2, then we can see it equals to Sn. (I don't think so!)