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Scientific Notation

# Scientific Notation - (1.21 0.05*10^2 =...

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Sheet1 Page 1 NATS 102 Home <index.html> Scientific Notation Courtesy of C. Keeton Astronomy deals with everything from atoms (0.0000000001 m) to the universe (100,000,000,000,000,000,000,000,000 m). To make it easier to write such small and large numbers we use /scientific/ (or /power of ten/) notation. ** *Simple powers of ten:* Write 1.0, and then move the decimal the number of spaces given by the exponent. 10^-3 = 0.001 10^-2 = 0.01 10^-1 = 0.1 10^0 = 1. 10^1 = 10. 10^2 = 100. 10^3 = 1000. ** *More complicated numbers:* Pull out the largest power of ten you can. The number left out front is called the /mantissa/. 390,100,000 = 3.901*100,000,000 = 3.901*10^8 0.00000558 = 5.58*0.000001 = 5.58*10^-6 ** *Addition and subtraction:* Make sure the exponents are the same, then just add or subtract the mantissas. 121+5 = (1.21*10^2 ) + (5*10^0 ) = (1.21*10^2 ) + (0.05*10^2 ) =

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Unformatted text preview: (1.21+0.05)*10^2 = 1.26*10^2 ** *Multiplication and division:* Simply multiply or divide the mantissas, and add or subtract the exponents. 121*50 = (1.21*10^2 ) * (5*10^1 ) = (1.21*5) * 10^2+1 = 6.05*10^3 250/50 = (2.5*10^2 ) / (5*10^1 ) = (2.5/5) * 10^2-1 = 0.5*10^1 = 5 300,000,000*31,000,000 = (3*10^8 ) * (3.1*10^7 ) = (3*3.1) * 10^8+7 = 9.3*10^15 Sheet1 Page 2 ** *Powers and square roots:* To raise a power of 10 to a power, multiply the two powers. (10^2 )^4 = 10^2*4 = 10^8 If you have a mantissa and a power of 10, raise both the mantissa and the power of 10. (2*10^2 )^4 = (2)^4 * (10^2 )^4 = 16 * 10^8 = 1.6 * 10^9 Taking the square root is equivalent to raising a number to the power 1/2. (900) = (9*10^2 ) ^1/2 = (9)^1/2 * (10^2 )^1/2 = 3 * 10 = 30...
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