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A large number is a polynomial in which the variable has the value 10.
The similarity is easy to see in
2478 = 2*103 + 4*102 + 7*101 + 8
and
2*x3 + 4*x2 + 7*x1 + 8
In multiplying large numbers, you would take the digits of one number, one by one, and multiply them into the digits of the other number. In each case, the product is given the place value that is the sum of the place values of the two digits.
Now, think of each digit in the number as the coefficient of the appropriate power of ten. And the two processes can be seen to be the same.
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Why would multiplying numbers in scientific notation be easier than multiplying them the regular way?
Multiplying numbers in scientific notation is easier when the numbers are very, very large or very, very small. Multiplying 0.000000000385 x 0.0000000474 is a pain. Multiplying 3.85 x 10-10 x 4.74 x 10-8 is not.
Can you have more then one outlier?
Yes. If you have a large group that is very similar and 2 or 3 that are not similar, the numbers that are not the same are all outliers
How does the Russian peasent algorithum work?
Russian Peasant Multiplication is a multiple-step replacement for multiplying large numbers. See the related link for an excellent explanation.
How is exponents are related to other subjects?
One use is shorthand for large numbers, eg the mass of the earth is 5960000000000000000000000 kg , which can be expressed as: 5.96 * 1024 kg there are also rules for multiplying / dividing exponential numbers
What is the area of a large rectangle?
The area of any rectangle, large or small, is calculated by multiplying length times width.
