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

by mr magoo
Tags: algrabraic, formula, process, repeated, times
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mr magoo
#1
Mar31-12, 02:27 PM
P: 23
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?
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jgens
#2
Mar31-12, 02:35 PM
P: 1,622
[itex]\frac{1}{2^5}[/itex]
mr magoo
#3
Mar31-12, 02:44 PM
P: 23
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

[itex]\frac{64}{2^{10}}[/itex]

mr magoo
#4
Mar31-12, 02:49 PM
P: 23
(1.0 / 2) process repeated 5 times; what is the algrabraic formula?

Thanks.
jgens
#5
Mar31-12, 02:50 PM
P: 1,622
That should actually be [itex]\frac{64}{2^{11}}[/itex].

Edit: Enclose your "10" in { } to make it appear correctly.
mr magoo
#6
Mar31-12, 02:52 PM
P: 23
Your right, I added one too many and thought there was only ten.
mr magoo
#7
Mar31-12, 02:59 PM
P: 23
Thanks for the editing tip.
Char. Limit
#8
Mar31-12, 04:31 PM
PF Gold
Char. Limit's Avatar
P: 1,951
Quote Quote by jgens View Post
[itex]\frac{1}{2^5}[/itex]
But that's not a formula.

[tex]\frac{1}{2^n}[/tex] is a formula.
jgens
#9
Mar31-12, 05:08 PM
P: 1,622
Quote Quote by Char. Limit View Post
But that's not a formula.
I could nitpick and argue that [itex]\frac{1}{2^n}[/itex] 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 [itex]\frac{1}{2^5}[/itex]. I really don't understand the objection.
Mentallic
#10
Apr1-12, 09:10 PM
HW Helper
P: 3,540
Quote Quote by mr magoo View Post
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

[itex]\frac{64}{2^{10}}[/itex]
Also notice that since we divided 64 by 2 five times and we got to 1, so [itex]\frac{64}{2^5}=1[/itex] rearranging, we get [itex]64=2^5[/itex] so we can express the answer as

[tex]\frac{64}{2^{10}}=\frac{2^5}{2^{10}}[/tex]

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

As we got in your first question.
rcgldr
#11
Apr2-12, 06:06 PM
HW Helper
P: 7,131
The formula (not sure if this is considered algebraic) or notation for a product series in the original example would be:

[tex]\prod_{i=1}^5 \ \frac{1}{2} [/tex]


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