Dividing large numbers


by Stratosphere
Tags: dividing, numbers
Stratosphere
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#1
Mar21-09, 04:08 PM
P: 360
How would you Divide very large numbers without using a calculator?
EX. [tex]\frac{125000}{299000000}[/tex]
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Helios
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#2
Mar21-09, 04:23 PM
P: 144
Long ago, before calculators, logarithms were used and invented for this purpose. You'd divide by subtracting logarithms and antilog the result to get the answer.
Santa1
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#3
Mar21-09, 05:40 PM
P: 104
One should usually first take out the obvious powers of ten, then factorize.

e.g.

[tex]\frac{125000}{299000000} = \frac{125}{299000}=\frac{5^3}{299\cdot 10^3} = \frac{5^3}{299\cdot (2\cdot 5)^3} = \frac{1}{299\cdot 2^3}[/tex]

And [tex]299\cdot 8 = 3 \cdot 10^2 \cdot 8 - 8 = 24 \cdot 10^2 - 8 = 2400 - 8 = 2392[/tex],

so that

[tex]\frac{125000}{299000000} = \frac{1}{2392}[/tex]

Which by hand is good enough for me.

(This might be wrong tho, it is kinda late here)

csprof2000
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#4
Mar22-09, 12:24 AM
P: 288

Dividing large numbers


"How would you Divide very large numbers without using a calculator? "

Long division is a correct algorithm. Are you asking whether or not there exists a faster way?
Stratosphere
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#5
Mar22-09, 12:35 PM
P: 360
Quote Quote by csprof2000 View Post
"How would you Divide very large numbers without using a calculator? "

Long division is a correct algorithm. Are you asking whether or not there exists a faster way?
Yes I am asking for a faster way.
qntty
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#6
Mar22-09, 01:02 PM
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P: 290
Quote Quote by Stratosphere View Post
without using a calculator?
Slide rule?
Count Iblis
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#7
Mar22-09, 01:49 PM
P: 2,159
You could use Newton-Raphson. Computing x = 1/y for given y amounts to solving the equation:

1/x - y = 0

Then, Newton-Raphson yields the following recursion for the nth approximation


x_{n+1} = x_n - (1/x_n - y)/(-1/x_n^2) =

x_n +x_n -y x_n^2 =

2 x_n - y x_n^2

The iteration doesn't involve any divisions, so it is a true division algorithm. The number of correct digits doubles after each iteration, while with long division you only get one decimal at a time, so it is much faster than long division.
Count Iblis
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#8
Mar22-09, 02:01 PM
P: 2,159
This is also an effective method:

http://en.wikipedia.org/wiki/Fourier_division


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