Today most school children use their calculators when multiplying and dividing large numbers. But their grandparents and even parents, however, had to use slide rules. Slide rules were devices that look a bit like several rulers connected. They weren't inches or centimeters. Instead, they were divided into lengths that represented logarithms. The logarithm of a number is the power to which you raise ten to get that number. For instance, the logarithm of two would be approximately equal to .3,
because ten to the three tenths power is approximately two (10^.3 = 2). Another example is that the logarithm of one is zero, because ten to the zeroth power equals one (10^0 = 1).
The reason that a slide rule works is because it adds the logarithms of numbers that are being multiplied, and subtracts the logarithms of numbers that are being divided. The sum of the logarithms of two numbers is the logarithm of the product of the two numbers (X Y = Z, LOG X + LOG Y = LOG Z). The same theory applies to dividing. The first number divided by the second number equals the quotient. The first number's logarithm minus the second number's logarithm equals the logarithm of the quotient (X / Y = Z, LOG X / LOG Y = LOG Z). Also, you can do squares and roots of numbers.
Suppose that you want to multiply 31 by 9. First, you set the one on the bottom of the middle ruler, the C scale (there are three rulers), on top of 31 on the bottom ruler, which looks like 3.1. Then, you move the sliding glass window so that the line down the center of it lines up with the 9 on the bottom of the middle ruler. The answer is where the line crosses the bottom ruler, in this case 279. (You must figure out for yourself where the decimal point goes because on a slide rule multiplying 31 by 9 is the same as 3100 times 90000 or .031 times .0009.) 
In the time between 1940 and 1970 the schools in the United States had slide rule competitions. These were contests where students were given complex problems and tried to solve them in short amounts of time. Each problem was worth five points. Two points were given for the first significant number, one for the second significant number, one for the third significant number, and one for putting the decimal in the right place. Exact numbers were impossible to get, but it didn't matter too much since slide rules were mainly used in engineering.
A lot has changed since the time of slide rules. Now, calculators and computers can solve equations with incredible speed, so that slide rules are no longer necessary.
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