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

Answer:

$3.5725 * 10^5$

Step-by-step 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

$\frac{x * 8}{8} = \frac{5 * 16 * 3.5725 * 10^4}{8}$

$x = \frac{5 * 16 * 3.5725 * 10^4}{8}$

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

$x = 10 * 3.5725 * 10^4$

$x = 3.5725 * 10^5$

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