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

In summary, the conversation discussed the repeated division of 1 by 2, resulting in the algebraic expression of 1 divided by 2 raised to the power of the number of divisions. This can also be expressed as a product series using the notation \prod_{i=1}^n \ \frac{1}{2} = \frac{1}{2^n}.
  • #1
mr magoo
23
0
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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  • #2
[itex]\frac{1}{2^5}[/itex]
 
  • #3
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]
 
Last edited:
  • #4
Thanks.
 
  • #5
That should actually be [itex]\frac{64}{2^{11}}[/itex].

Edit: Enclose your "10" in { } to make it appear correctly.
 
  • #6
Your right, I added one too many and thought there was only ten.
 
  • #7
Thanks for the editing tip.
 
  • #8
jgens said:
[itex]\frac{1}{2^5}[/itex]

But that's not a formula.

[tex]\frac{1}{2^n}[/tex] is a formula.
 
  • #9
Char. Limit said:
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.
 
  • #10
mr magoo said:
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.
 
  • #11
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]
 
Last edited:

1. What is the purpose of repeating the (1.0 / 2) process 5 times?

The purpose of repeating the (1.0 / 2) process 5 times is to observe how the value changes with each repetition and to determine any patterns or trends.

2. How do you calculate the result of repeating the (1.0 / 2) process 5 times?

The result of repeating the (1.0 / 2) process 5 times can be calculated by using the algebraic formula (1/2)^n, where n represents the number of repetitions.

3. What is the significance of the number 5 in this process?

The number 5 is the number of repetitions in the (1.0 / 2) process. It is a small but sufficient number to observe any patterns or trends in the values.

4. Can the (1.0 / 2) process be repeated more or less than 5 times?

Yes, the (1.0 / 2) process can be repeated any number of times. However, repeating it less than 5 times may not provide enough data to determine any patterns, while repeating it more than 5 times may not significantly change the results.

5. What type of data or values can be obtained from repeating the (1.0 / 2) process 5 times?

By repeating the (1.0 / 2) process 5 times, data on the changing values can be obtained, and the overall trend can be determined. This can be useful in various scientific experiments and studies.

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