Lesson 42: Estimating with Scientific Notation

The scientific notation problems we have encountered thus far have been carefully designed so the numbers multiply and divide easily, and so the first part of the answer is an integer. Unfortunately, real life problems contain numbers that are not so easy to handle.

For instance, the answer to the last example in Lesson 41 was (16)(5280)(5280)(5280)(12)(12)(12) in. cubed. Multiplying these numbers by hand would be tedious, and we might make a mistake. If we use a calculator that does not have scientific notation, we get an error notation early because the answer is a number too large to handle.

If we use a calculator that has scientific notation we would get x 10. however, we will find that we often make mistakes when we use calculator for complicated operations such as this one. Thus we need to develop a way to see if the answer is reasonable, and we should be able to estimate the answer when a calculator is not available. 15

In this problem, we should be able to estimate an answer between 4 x 10 and 4 x 10. this would let us know that our calculator answer of x 10 is a reasonable answer

Example: Estimate this product: (16)(5280)(5280)(5280)(12)(12)(1 2)

Answer: (2 x 10 )(5 x 10 )(5 x 10 )(5 x 10 )(1 x 10 )(1 x 10 )(1 x 10 ) 2(5)(5)(5) x 10 = 250 x 10 Is about 3 x 10 Our calculator answer is probably correct from our estimation

Example: Use scientific notation to help estimate the answer to this problem. (3728)(470,165 x 10 ) (278,146)( x 10 )

Answer: (4 x 10 )(5 x 10 ) (3 x 10 )(7 x 10 ) About 1 x

Example: Use scientific notation to help estimate the answer to this expression. ( x 10 )(41,725 x 10 ) 9764 x

Answer: (4 x 10 )(4 x 10 ) 1 x 10 About 2 x

HW: Lesson 42 #1-30