Big Number MultiplicationDate: 05/04/97 at 20:33:23 From: Victor Yoon Subject: Multiplication Dr. Math, What does 4000*500*32*768*4 equal? 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 answer is 196608000000. 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/ |
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