# Dividing large numbers

by Stratosphere
Tags: dividing, numbers
 P: 360 How would you Divide very large numbers without using a calculator? EX. $$\frac{125000}{299000000}$$
 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.
 P: 104 One should usually first take out the obvious powers of ten, then factorize. e.g. $$\frac{125000}{299000000} = \frac{125}{299000}=\frac{5^3}{299\cdot 10^3} = \frac{5^3}{299\cdot (2\cdot 5)^3} = \frac{1}{299\cdot 2^3}$$ And $$299\cdot 8 = 3 \cdot 10^2 \cdot 8 - 8 = 24 \cdot 10^2 - 8 = 2400 - 8 = 2392$$, so that $$\frac{125000}{299000000} = \frac{1}{2392}$$ Which by hand is good enough for me. (This might be wrong tho, it is kinda late here)
P: 290

## 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?
P: 360
 Quote by csprof2000 "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.
P: 290
 Quote by Stratosphere without using a calculator?
Slide rule?
 P: 2,141 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.
 P: 2,141 This is also an effective method: http://en.wikipedia.org/wiki/Fourier_division

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