When you have a fraction, meaning you are dividing one number by another, you can always move the decimal point in both numbers, provided you move it the same number of places in each number (both numerator, and denominator), and in the same direction.
Now, when you are multiplying two numbers, you can always move the decimal point in both of them, provided you move it the same number of places in each factor, and in the opposite direction.
These two manipulations can significantly simplify the given operation.
Learning from historical mistakes
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The following extraordinary paragraph comes from Knuth’s TAOCP Volume 4A,
right before the last set of exercises. Many of the exercises below ask a
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