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-   -   (1.0 / 2) process repeated 5 times; what is the algrabraic formula? (http://www.physicsforums.com/showthread.php?t=592196)

 mr magoo Mar31-12 02:27 PM

(1.0 / 2) process repeated 5 times; what is the algrabraic formula?

1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.0625
0.0625 / 2 = 0.03125

What is the algebraic formula for this?

 jgens Mar31-12 02:35 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

$\frac{1}{2^5}$

 mr magoo Mar31-12 02:44 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

This is a new one;

64 / 2 = 32
32 / 2 = 16
16 / 2 = 8
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1
1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.0625
0.0625 / 2 = 0.03125

$\frac{64}{2^{10}}$

 mr magoo Mar31-12 02:49 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Thanks.

 jgens Mar31-12 02:50 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

That should actually be $\frac{64}{2^{11}}$.

Edit: Enclose your "10" in { } to make it appear correctly.

 mr magoo Mar31-12 02:52 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Your right, I added one too many and thought there was only ten.

 mr magoo Mar31-12 02:59 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Thanks for the editing tip.

 Char. Limit Mar31-12 04:31 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Quote:
 Quote by jgens (Post 3843560) $\frac{1}{2^5}$
But that's not a formula.

$$\frac{1}{2^n}$$ is a formula.

 jgens Mar31-12 05:08 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Quote:
 Quote by Char. Limit (Post 3843727) But that's not a formula.
I could nitpick and argue that $\frac{1}{2^n}$ is actually an expression and not a formula since it does not contain an equals sign; but the distinction is really not all that relevant. The OP wanted to know how to express "1 divided by 2 fives times" algebraically and one way is $\frac{1}{2^5}$. I really don't understand the objection.

 Mentallic Apr1-12 09:10 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Quote:
 Quote by mr magoo (Post 3843573) This is a new one; 64 / 2 = 32 32 / 2 = 16 16 / 2 = 8 8 / 2 = 4 4 / 2 = 2 2 / 2 = 1 1 / 2 = 0.5 0.5 / 2 = 0.25 0.25 / 2 = 0.125 0.125 / 2 = 0.0625 0.0625 / 2 = 0.03125 $\frac{64}{2^{10}}$
Also notice that since we divided 64 by 2 five times and we got to 1, so $\frac{64}{2^5}=1$ rearranging, we get $64=2^5$ so we can express the answer as

$$\frac{64}{2^{10}}=\frac{2^5}{2^{10}}$$

And if you remember the rule of indices, $$\frac{2^a}{2^b}=2^{a-b}$$ so $$\frac{2^5}{2^{10}}=2^{5-10}=2^{-5}=\frac{1}{2^5}$$

As we got in your first question.

 rcgldr Apr2-12 06:06 PM

Re: (1.0 / 2) process repeated 5 times; what is the algrabraic formula?

The formula (not sure if this is considered algebraic) or notation for a product series in the original example would be:

$$\prod_{i=1}^5 \ \frac{1}{2}$$

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