Friday, August 6, 2010

19871988

It was the year 1987, and I have encountered this (homework?) problem. Calculator is allowed.
The problem is this: Evaluate 19871988. Give 4 significant digits in scientific notation.

Whoa, my calculator can't handle a number this big! Yours probably can't either.

But WHOA, Windows' calc can handle that. Amazing.
The answer is 6.567e+6556

How do you get this without a calculator that can have this big capacity? The answer is... logarithm.

Let x = 19871988.

log both sides, bring that exponent down.

log x = 1988 log 1987

The right hand side is: 6556.81735

This means, x = 10^(6556.81735).

The exponent is 6556.

The mantissa is 10^(0.81735) = 6.567.

Isn't it pleasing to find a use of that [10^x] key?

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