Start by writing the weight of the bag of sand in grams.
10^7
Practice makes perfect
We know that the mass of a grain of sand is about 10^(- 3) grams. We want to calculate the approximate number of grains of sand in a 10-kilogram bag of sand. To compare two values, both of them should be expressed in the same unit. We will start by writing the weight of the bag of sand in grams.
Unit of Weight
Weight (grams)
Weight as a Power
Kilogram
1000
10^3
We can see that a kilogram is 10^3 grams. Using this value we can rewrite the weight of the sand bag in grams.
10 kilograms = 10 * 10^3 gramsLet's evaluate the weight of the sand bag in grams. First, we will rewrite 10 as a power 10^1.
10 kilograms = 10^1 * 10^3 grams
Now, we have a product of powers with the same base. We can use the Product of Powers Property to simplify this expression.
We know the weight of the bag of sand in grams and we know the mass of a grain of sand. Next, we can divide the weight of the bag by the mass of one grain. By doing that, we will find the approximate number of grains of sand in the bag.
10^4 grams/10^(- 3) grams
Now, we have a quotient of powers with the same base. Let's use the Quotient of Powers Property to calculate this quotient. We have negative exponents but this property works also for negative exponents. We can forget about units for a moment for simplicity.
