Question

There are about 3.5725 * 10^4 grains of sand in an 8-ounce cup. Based on this, about how many grains of sand would there be in a 5-gallon container (note: 1 gallon = 16 cups). Write the result in scientific notation.

Answer 1

`3.5725 * 10^5`

Explanation:

Given

There are about 3.5725 * 10^4 grains of sand in an 8-ounce cup.

Required

How many grains of sand would there be in a 5-gallon container?

Let x represent the number of grains in 5 gallon; So, From the question, we have that;

8 cups = 3.5725 * 10^4

5 gallon = x

Cross Multiply

x * 8 cups = 5 gallon * 3.5725 * 10^4

Recall that 1 gallon = 16 cups

`x * 8\ cups = 5 * 16\ cups * 3.5725 * 10^4`

`x * 8 = 5 * 16 * 3.5725 * 10^4`

Divide both sides by 8

`(x * 8)/(8) = (5 * 16 * 3.5725 * 10^4)/(8)`

`x = (5 * 16 * 3.5725 * 10^4)/(8)`

`x = 5 * 2 * 3.5725 * 10^4`

`x = 10 * 3.5725 * 10^4`

`x = 3.5725 * 10^5`

Hence, the number of grains of sand in 5 gallon is
`3.5725 * 10^5`