EXPONENTIAL NATATION

• Exponential notation, also known as scientific notation, is one way to write very large or very small numbers. A number in exponential notation is written as the product of either a decimal or an integer, and a power of 10. This works because in our base-10 place value system, each place value column is 10 times larger than the one before it when you move from right to left. When moving from left to right, each place value column is ten times smaller than theone before it. This “times 10” relationship between the columns makes it possible to represent numbers in exponential notation. An exponent, a small number written up to the immediate right of the 10 tells which power is being used. In other words, the exponent tells how many place value columns are being represented. 
•  Although this way of writing numbers may sound confusing when you read its explanation, examples quickly make it more clear. 10 can be represented as 1 x 101 (This is like saying 1 x 10). 100 can be represented as 1 x 102 (This is like saying 1 x 10 x 10). 1,000 can be represented as 1 x 103 (This is like saying 1 x 10 x 10 x 10). 10,000 can be represented as 1 x 104 (This is like saying 1 x 10 x 10 x 10 x 10). For each place value column, add one more number to the exponent. So far, our base number has been 1. It can be another wholenumber, like 4. The number 4,000,000,000 can be represented in exponential notation as 4 x 106. This is a shorthand way of saying 4 x 10 x 10 x 10 x 10 x 10 x 10. You will also notice that the exponent matches the number of zeroes on the original number.
• The base number can even be a decimal, although some care needs to be taken to make sure the decimal point is considered correctly. For example, you might see 4.5 x 104. Be careful. When you convert the number 4.5 x 104  from exponential to standard notation (writing it in standard number form) it becomes not 450,000 but rather 45,000. Moving the decimal point one place value space to the right replaces one of the zeroes. The more familiar you become with exponential notation, the more fun it will become. Math is kind of like playing with numbers. The more you know, the more fun it is.

 Name:__________________________________

Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers.

1)   Based on what you have read, why is our number system called a base-10 system? 

   2)   When do you think it would make sense to write a number using exponential notation?

   3)   What is the main idea of this passage?

   4)   What is the relationship between each of the place value columns?

   5)   What is a base number?