# long decimal division

Discussion in 'Math' started by amilton542, Jan 22, 2011.

1. ### amilton542 Thread Starter Active Member

Nov 13, 2010
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anybody know an easy method for long decimal division without a calculator. for e.g 0.0678945 / 0.0004567

2. ### Georacer Moderator

Nov 25, 2009
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You can rewrite the fraction as $\frac{0.0678945}{0.0004567}=\frac{678945}{4567} \cdot \frac{10^{-7}}{10^{-7}}=\frac{678945}{4567}$
but you still have to divide the significant figures by hand.

amilton542 likes this.

Jul 7, 2009
1,585
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In the old days when there were no electronic or mechanical calculators, there were basically three ways to do such problems:

1. Do it long hand like you were taught in school. The method works for any numbers.

2. Do it with a slide rule. Gives around 3 significant figures. Only the mantissas are calculated; you need to figure out where the decimal point should be.

3. Do it with logarithms. This is usually faster than long hand and just involves addition and subtraction. With the usually-available tables, could get you around 5 significant figures.

There are a variety of tips and approximations to help get the answer.

The key to help you choose which method to use depends on how many significant figures you want in the answer. It's not very often you need more than 4 or 5, which explains why logarithms were a popular method for centuries.

Nov 9, 2007
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5. ### Georacer Moderator

Nov 25, 2009
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1,266
I love that system... Especially when it's combined with a Eurotrip: