Often times we do not want to sit and calculate the solution to a problem because it might not be worth our time.

For example, suppose I went to a grocery store and had $20 to spend on groceries and I picked up the following items.

Items PricesMilk $4.05

Bread $2.99

Cereal $3.69

Grapes $6.07

Cheese $4.99

Suppose I wanted to determine if I could afford all the items, how would I go about doing so?

I could add these prices up and get an exact answer, but that to me seems like it would take more time than it is worth.

Another, much quicker, method would be to round the prices to whole numbers in my head and then add those numbers up.

Items Prices Estimated Prices

Milk $4.05 $4

Bread $2.99 $3

Cereal $3.69 $4

Grapes $6.07 $6

Cheese $4.99 $5

The estimated cost of the items is $22.

Rounding the prices and adding them together like this gives a quick way to determine that I would be going over budget.

We perform estimations in physics when we want to check the validity of a calculation.

Using estimation can help us check our expected value against the value given in a calculation.

When these values are vastly different it alerts us that something went wrong, either in our estimation or our calculation.

Suppose we wanted to estimate the distance between the Earth and the Moon.

If we estimated that this distance should be hundreds of thousands of miles, but our calculation showed that it was only one hundred miles, this would tell us that something needed to be checked.