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### Big Number Multiplication

```
Date: 05/04/97 at 20:33:23
From: Victor Yoon
Subject: Multiplication

Dr. Math,

What does 4000*500*32*768*4 equal?
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```
Date: 05/05/97 at 03:21:26
From: Doctor Mike
Subject: Re: Multiplication

Hi Victor,

I'm just going to do this on my calculator, but in a way that will not
give such a big number that it will cause an overflow.

I am going to factor out some powers of ten so as to make the numbers
a little smaller for the calculator. That comes out as:

4 * 1000 * 5 * 100 * 32 * 768 * 4  =

4 * 5 * 32 * 768 * 4 * 1000 * 100

I will ask the calculator to find 4*5*32*768*4 and then I will add 5
zeros onto the end.  That is because 1000*100 is 10 to the 5th power,
and each time you multiply by 10, it adds a zero onto the right end of
the product.

Actually, I'm just seeing that the 4*5 at the start equals 20, so I am
going to re-write this calculation as follows:

20 * 32 * 768 * 4 * 1000 * 100  =

2 * 32 * 768 * 4 * 10 * 1000 * 100

I will ask the calculator to find 2*32*768*4 and then I will add 6
zeros onto the end. That is because 10*1000*100 is 10 to the 6th
power.  Actually, there is one more thing I want to do before I pull
out the calculator. If there is something I can do in my head before
I start to push the keys, I like to do that, since sometimes the keys
stick and I want to minimize the chance for a mistake.

I know, and you probably do too, that as long as all you're doing is
multiplication, you can multiply numbers together in any order, so I'm
going to re-arrange them and do some stuff in my head. It comes out
like this:

2 * 4 * 32 * 768 * 10 * 1000 * 100  =

8 * 32 * 768 * 10 * 1000 * 100

Now I use the calculator to find that 8*32*768 = 196608 so the full

If you write this with commas it looks like 196,608,000,000, which is
a number between 196 billion and 197 billion.  By the way, what were
you counting?  Or was this a big problem you just thought of?

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication

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