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(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:

`(5\cdot10^(-5))/(10^(-9))nm`

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

`5\cdot(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.