Chemistry, find the mass, and put in scientific notation word problem.

Question

The density of a certain type of plastic is 0.91 g/cm³. If a sheet of this plastic is 10.0 m long, 1.0 m wide, and 1 cm thick, what is its mass?

 

mass = _____ X 10^_____g

Enter your answer in scientific notation.

PLEASE HELP

Answer 1

This problem can be solved through Dimensional Analysis and understanding base 10 rules: I would first convert everything to scientific notation and convert (cm to m) as done below

10m = 1 x 10⁴ m

1m = 1 x 10³ m

1cm = 1 x 10^-2 m

I would then multiply coefficients and add exponents ( 1 x10⁴) ( 1 x 10³) (1 x 10^-2)

example of multiplying coefficients ( 1 x 1 x 1) = 1

adding the exponents ( 4 + 3 + -2) = 5

So the volume of the material ( L x W x H) becomes ( 1x 10⁵), now we are ready to multiply by the density of the plastic 0.91 g/cm³

(0.91 g/cm³) x ( 1 x 10⁵) = 0.91 x 10⁵ but WAIT, we are not done yet. We have to put the answer is proper scientific notation, and in doing so the coefficient will be a single number between 1-9

so we multiply our coefficient by 10 (making the coefficient bigger) and we divide our exponent by 10 (making the exponent smaller)

and our final answer will be: 9.1 x 10⁴g

Answer 2

Use dimensional analysis. To find the mass we want to use the density and the volume. We will multiply the density by the volume to get the mass, as in g/cm³ x cm³ = g.

Density = 0.91 g / cm³

Volume of material = L x W x H (note that the H or thickness is given in cm but others are in m. So we will

change the L and W from m to cm before doing the calculation, since we want our volume to be in cm³)

L = 10.0 m x 100 cm / m =1000 cm

W = 1.0 m x 100 cm / m = 100 cm

H = 1 cm

Volume = 1000 cm x 100 cm x 1 cm = 100000 cm³ = 1x10⁵ cm³

Now we can use the density and the volume to solve for the mass:

0.91 g / cm³ x 1x10⁵ cm³ = 9.1x10⁴ g