Scientific Notation

Quick Scientific Notation Review

Since we'll be working with very large and very small numbers, we'll be using scientific notation to cut down on all of the zeroes we need to write. As a quick review:

10 = 1*10^1, 253 = 2.53*100 = 2.53*10^2, and 15,000,000,000 = 1.5*10^{10} which you'll see sometimes written as 15*10^9 even though this is not proper scientific notation. For small numbers we have: 1/10 = 1*10^{-1}, 1/253 = 1/(2.53*100) = 1/2.53 *10^{-2} or about 0.395*10^{-2} = 3.95*10^{-3} and (3*10^{10})/(6*10^{23}) = 3/6 * 10^{10-23} = 0.5*10^{-13} = 5*10^{-14}. The last example shows that you subtract exponents when you divide numbers. If the number had been (3*10^{10})*(6*10^{23}), you'd have 3*6*10^{10+23} = 18.*10^{33} = 1.8*10^{34}. You add exponents if you multiply numbers. You subtract one from the exponent for every space you move the decimal to the right. You add one to the exponent for every space you move the decimal to the left.

Most scientific calculators work with scientific notation. Your calculator will have either an ``EE'' key or an ``EXP'' key. That is for entering scientific notation. To enter 253 (= 2.53*10^2), you would punch 2  .  5  3  EE or EXP  2. To enter 3.95*10^{-3}, you would punch 3  .  9  5  EE or EXP  3  [+/- key]. Note that if the calculator displays ``3.53 -14'' it means 3.53*10^{-14} NOT 3.53^{-14}! Also if you have the number 4*10^3 and you enter 4  x  10  EE or EXP  3, the calculator will interpret that as 4*10*10^3 = 4*10^4 or ten times the number you really want!

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last updated 29 Aug 95


Nick Strobel -- Email: strobel@astro.washington.edu

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Astronomy
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