Example:

Bob told Mary that his department had 400 times the productivity of her department. Mary immediately suspected that John's figures were incorrect. How did she know?

Mary learned that it is easy to make big mistakes with her calculations when she learned to evaluate expressions , so she decided to question Bob's figures. Even though she did not have the income figures for Bob's department, she knew that he had 1/2 as many employees as her department. She also knew that her department's productivity was quite good. She estimated Bob's department could not have a productivity 400 times that of her department.

Examples:

1. Estimate the number of telephones required by a department of 170 people.

Common sense tells us that each person in the department will need a telephone and some people will need two. We can estimate that the department will need around 200 telephones.

2. Estimate the number of coffee cups that will fit on a 2 foot by 3 foot shelf.

To make this estimate we need more than common sense. We need to know how approximately how much room a cup takes up on a shelf and how to find the area of the shelf. The area of the shelf is 2 * 3 = 6 square feet and a cup takes up about 1/3 * 1/3 = 1/9 square foot. So about 9 cups fit in each square foot and 9 * 6 = 54, so at least 54 cups will fit on the shelf.

3. Estimate the number of office cubicles that a room 20 feet by 20 feet can be divided into.

For this estimate to be very accurate, we need to know how much room a desk and chair take and how much room is required for hallways, etc. However, even without such information we know that 200 cubicles would be too many and 5 cubicles would be too few.

Round off the numbers in the problem so you can do the arithmetic more easily.

Practice estimating the result of multiplication and division problems. If you multiply a 2-digit number by a 2-digit number, you will get a 3- or 4-digit number. This idea is covered in the Exponents and Logarithms station.