Chapter 1

1. (a) 8.69 x 104 = 86,900.

        (b) 7.1 x 103 = 7,100.

        (c) 6.6 x 10-1 = 0.66.

        (d) 8.76 x 102 = 876.

        (e) 8.62 x 10-5 = 0.000 086 2.

2. (a) Assuming the zeros are not significant, we have 1,156,000 = 1.156 x 106.

        (b) 218 = 2.18 x 102.

        (c) 0.0068 = 6.8 x 10-3.        

        (d) 27.635 = 2.735 x 101.

        (e) 0.21 = 2.1 x 10-1.

        (d) 22 = 2.2 x 101.

3. % uncertainty = [(0.25m)/(2.26m)] 100 = 11%.

        Because the uncertainty has two significant figures, the % uncertainty has 2 significant figures.

4. We assume an uncertainty of 1 in the last place, i.e., 0.01, so we have

           % uncertainty = [(0.01)/(1.67)] 100 =  0.6%.

        Because the uncertainty has 1 significant figure, the % uncertainty has 1 significant figure.   

5.  For multiplication, the number of significant figures in the result is the least number from the multipliers; in this case 2 from the second value.

            (2.079 x 102m)(0.072 x 10-1) = 0.15m.

6. To add, we make all of the exponents the same:

            7.2 x 103s + 8.3 x 104s + 0.09 x 106s = 0.72 x 104s + 8.3 x 104s + 9 x 104s

                                                                       = 18.02 x 104s = 1.802 x 105s.

7. We assume an uncertainty of 0.1 x 104cm. We compare the area for the specified radius to the area for the extreme radius.

             A1 = pR12 = p(2.8 x 104cm)2 = 2.46 x 109cm2;  

            A2 = pR22 = p[(2.8 +0.1) x 104cm]2 = 2.64 x 109cm2,

        So the uncertainty in the area is DA = A2 - A1 = = 0.18 x 109cm2 = 0.2 x 109cm2.

        We write the area as  A = (2.5 + 0.2) x 109cm2.

8. We compare the volume with the specified radius to the volume for the extreme radius.

            V1 = 4/3pR13 = 4/3p(3.86m)3 = 241m3,   V2 = 4/3pR23 = 4/3p(3.86 + 0.08m)3 = 256m3.

         So the uncertainty in the volume is DV = V2 - V1 = 15m3; and the % uncertainty is

            % uncertainty = [(15m3)/(241m3)] 100 =  6%.

9. (a) 106volts = 1 megavolt = 1Mvolt.

        (b) 10-6meters = 1 micrometer = 1mm.

        (c) 5 x 103days = 5 kilodays = 5 kdays.

        (d) 8 x 102bucks = 8 hectobucks = 0.8kbucks.

        (e) 8 x 10-9pieces = 8 nanopieces = 8npieces.

10. To add, we make all of the units the sme:

            1.00m + 142.5cm + 1.24 x 105mm = 1.00m + 1.425m + 0.124m

                                                                   = 2.549m =  2.55m

11. (a) 7800 = 7.8 x 103 = 10 x 103 =  104.

          (b) 9.630 x 102 = 10 x 102 =  103.

          (c) 0.0076 = 0.76 x 10-3 =  10-3.

          (d) 150 x 108 = 1.50 x 1010 =  1010.

 

 

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