This math question ..?

Question

I'm having trouble solving this.. it's about scientific notation and exponents:

Wavelengths of light are measured in Angstrom units. AN Angrstrom unit is 10^ -8cm. The wavelength of Cadmium's green line is 5085.8 Angrstrom units. How many wavelengths of Cadmium's green line are there in one meter?

Also, Metal expands and contracts with changes in temperature. THe change in the length of steel per degree Celsius is given by the constant 11 x 10^ - 6. A steel bridge 200 meters long varies in temperature 70 degrees Clesius. What is the change in the length of the bridge in centimeters? Thanks! please tell me the steps to solving it too!

Answer 1

1 m=100 cm=10^2 cm..The wavelength of Cadmium is 5085.8X10^-8.Therefore the no. of wavelengths in a meter=(10^2)/5085.8X10^-8= 5085.8X10^(2+8)=5085.8X10^10 (you may write it as 5..0858X10^13)
The co-efficient of linear expnsion of the metl is given as11X10^-6.As the length of the bridge is given as 300 meters and the increase of temp. as 70 degrees ,the expnsion would be 300X70X11X10^-6 or 3X10^2X7X10^1X1.1X10^1 X11X10^-6X10^2 cm=3X7X1.1X11X10^(^2+1+1-6+2)=254.1X10^0
=254.1 cm

Answer 2

1A is 1x10e-10m this means 0,0000000001 m
The cadmium's line is 5085.8A so it is 5085.8x10e-10m which is 0,00000050858m. To know how many there are in one meter, just divide 1 by that number, so 1/0,00000050858

for the bridge, the coefficient 11x10e-6 means that every meter of that bridge will expand 0,000011m for each degree the temperature rise. To calculate the total variation in length, multiply the coefficient x length x temperature rise so 0,000011x200x70. Don't forget to then add that variation to the 200m.

So if the scientific notation is you trouble, just remember that this little number there, the exposant, is the number of of place the decimal point has been moved. 5x10e-3 is 0,005 because the decimal point is three positions behind its actual place.