So I'm discussing the number of atoms in the universe with a nice chap, but we can't seem to agree. Google told me the answer to be 10^82. He says it's 6x10^82. He says the six isn't relevant with a number so vast.
To my mind the exponent doesn't negate the six. But I am not a mathematician.
- 6x1 is not approximately 1
- 6x10 is not approximately 10
- 6x100 is not approximately 100
So how can six of any number, however enormous, be approximately the same as one times? It would appear to this untrained eye that the exponent makes the approximation worse, not better.
Please will someone explain this to me? Thanks in advance, and please understand - I'm not asking this so I can go back and bedazzled him with superior unearned intellect, nor hate on him either. I'm just a curious person.
When dealing with large numbers like the number of atoms in the universe it's common use as an estimate the number of decimal places needed. That's the exponent when you write the number in scientific notation, so roughly the number of zeroes. It's (approximately) the (base $10$) logarithm of the number.
So you and your friend are both right, using different conventions. Six times as much is indeed larger. But for a number with $82$ zeroes, multiplying by $6$ might add one more zero. So only about an $8\%$ change when you measure that way.