Question

A sheet of paper is 0.00005 meter thick. One nanometer is 1 x 10^-9 meter. how thick is a sheet of paper in nanometers

Answer 1

Since 1 nanometer = 1x10^-9 meter, then, use the conversion factor:

$\frac{1nm}{10^{-9}m^{}}$

Multiply the thickness of the sheet of paper measured in meters times the conversion factor:

$(0.00005m)\cdot\frac{1nm}{10^{-9}m}$

Rewrite 0.00005 in scientific notation by moving the point 5 places to the right:

$0.00005=5\cdot10^{-5}$

The thickness of the sheet of paper, is:

$\frac{5\cdot10^{-5}}{10^{-9}}nm$

Use the laws of the exponents to rewrite 10^-5/10^-9:

$5\cdot\frac{10^{-5}}{10^{-9}}nm=5\cdot10^{-5-(-9)}nm=5\cdot10^{-5+9}nm=5\cdot10^4nm$

Rewrite 5x10^4 nm by moving the point 4 places to the right:

$5\cdot10^4nm=50,000nm$

Therefore, the thickness of a sheet of paper is 50,000 nm.