College

The average mass of a grain of sand is [tex]1.5 \times 10^{-5}[/tex] grams. Erin's sandbox has approximately [tex]3.067 \times 10^{11}[/tex] grains of sand in it. What is the mass of the sand in Erin's sandbox?

Answer :

The mass of the sand in Erin's sandbox is calculated by multiplying the mass of a single grain (1.5 x 10^-5 grams) with the number of grains (3.067 x 10^11), yielding 4.6005 x 10^6 grams or 4600.5 kilograms.

To calculate the mass of the sand in Erin's sandbox, we need to multiply the average mass of a single grain of sand by the total number of sand grains. The average mass of a grain of sand is 1.5 x 10^-5 grams, and the sandbox contains approximately 3.067 x 10^11 grains of sand.

Using multiplication for scientific notation, we calculate:

Mass of single grain of sand x Number of sand grains = Total mass

(1.5 x 10^-5 grams) x (3.067 x 10^11) = 4.6005 x 10^6 grams

Converting grams into kilograms (since there are 1000 grams in one kilogram), the total mass in kilograms is:

4.6005 x 10^6 grams \/ 1000 = 4600.5 kilograms

Therefore, the mass of the sand in Erin's sandbox is 4600.5 kilograms.

Answer:

4.6005 * 10^6 grams

Step-by-step explanation:

Average mass of sand grain = 1.5 * 10^-5 grams

Number of grains in Erin's sandbox = 3.067 * 10^11 grains

To obtain the mass of sand in Erin's grain box :

We multiply the mass per sand grain and the number of grains

(1.5 * 10^-5) * (3.067 * 10^11)

1.5 * 3.067 = 4.6005 * (10^(-5+11))

4.6005 * 10^6 grams