excel hw
CEEZEEF
7_ws5_scientific_notation_worked_examples.docxPhysics – Scientific Notation Examples Name: ___________________________
Mr. Sidor Period: _______ Date: ______________
Examples of multiplication using scientific notation and maintaining the correct number of significant figures in result. 4 1
1. 12.12 x 300 Write # significant digits above values
= 1.212 x 101 x 3 x 102 Write numbers in scientific notation
= 1.212(3) x 101 x 102 Collect Mantissa and exponents
= 3.636 x 103 Multiply mantissas, add exponents
= 4 x 103 Report result to smallest # of significant digits of any input.
Notice had to round up from 3.6 to 4 in this example.
Note: This mantissa result was less than 10 so one did not have to pull out a 10.
4 3 4 3
2. 0.6000 x 40200 3. 0.0002300 x 0.0200 x
= 0.6000x10-1 x 4.02 x 104 = 2.300 x 10-4 x 2.00 x 10-2
= 6(4.02) x 10-1 x 104 = 2.3(2) x 10-4 x 10-2
= 24.12 x 103 = 4.6 x 10-6
= 2.412 x 101 x 103 = 4.60 x 10-6 (3 Sig. Figs.)
= 2.412 x 104
5 3 4 2
4. 20110. x 0.00500 5. 0.08324 x 0.00020
= 2.0110 x 104 x 5.0 x 10-3 = 8.324 x 10-2 x 2.0 x 10-4
= 2.011(5) x 104 x 10-3 = 8.324(2) x 10-2 x 10-4
= 10.055 x 101 (Pull out 10) = 16.648 x 10-6 (Pull out 10)
= 1.0055 x 101 x 101 = 1.6648 x 101 x 10-6
= 1.0055 x 102 (Round up) = 1.6648 x 10-5(Round up)
= 1.01 x 102 (3 Sig. Figs.) = 1.7 x 10-5 (2 Sig. Figs.)
Examples of adding using scientific notation and maintaining the correct number of significant figures in result.
6. 4.4444 x103 + 4.44x102 I choose 102 as base. Could have chosen 103 or 100
= 4.4444 x103 (10-1 x 101) + 4.44x102 Figure what is needed to get to 102
= 4.4444 x 102 x 101 + 4.44 x 102 Multiply through by any excess exponent
= 44.444 x 102 + 4.44 x 102 Now use normal addition on mantissa
44.444 x 102 Align decimal and add “chop” + 4.44 x 102
48.88444 x 102 Note that exponents are not added,
= 48.88 x 102 instead they remain the same.
= 4.888 x 103 Need to pull out ten in this case.
7. 2.222 x 10-3 + 1.111 x 10-4 8. 8.88888 x 103 - 3.33 x 10-2
= 2.222x10-3 (10-1x101) +1.111x10-4 = 8.88888 x 103(10-5x105) - 3.33 x 10-2
= 2.222 x 10-4 (101) + 1.111 x 10-4 = 8.88888 x 10-2 x105 - 3.33 x 10-2
= 22.22 x 10-4 + 1.111 x 10-4 = 888888. x 10-2 - 3.33 x 10-2
22.22 x 10-4 888888. x 10-2 + 1.111 x 10-4 – 3.33 x 10-2
23.331 x 10-4 888884.67 x 10-2
= 2.333 x 101 x 10-4 = 8.88885 x 10-2 x 105 (Round up)
= 2.333 x 10-3 = 8.88885 x 103
9. 1.111 x 102 + 3.33 x 105 10. 6.66 x 10-2 + 5.5555 x 102
= 1.111 x 102 (103x10-3) +3.33 x 105 = 6.66 x 10-2(104x10-4) + 5.5555 x 102
= 1.111 x 105 (10-3) +3.33 x 105 = 6.66 x 102 x10-4 + 5.5555 x 102
= 0.001111 x 105 + 3.33 x 105 = 0.000666 x 102 + 5.5555 x 102
0.001111 x 105 0.000666 x 102 + 3.33 x 105 +5.5555 x 102
3.331111 x 105 5.556166 x 102
= 3.33 x 105 = 5.5562 x 102 (Round up)
