Algebra 1 CH 8.4 Use Scientific Notation.notebook
Use Scientific Notation
April 30, 2015
Use Scientific Notation
Scientific Notation
Objective:Read and write numbers in scientific notation. Convert numbers from scientific notation to standard notation and vice versa. Multiply and divide numbers in scientific notation.
Feb 16­3:54 PM
Use Scientific Notation
Big Numbers
For a large number such as 900,000 we will be moving the decimal point to the left so that we have a number greater than or equal to one, but less than ten. The decimal point is moved 5 places to the left, and this is an important number to remember, because this is going to be the power we use with 10. Since we now have found that 9 is our number between 1 and 10 and our power which is 5, we can now write 900,000 in scientific notation as: 9 x 105
If we have a number such as 456,000,000 we use the same
process. The decimal point is moved to the left until we get a number that is between 1 and 10. When we move our decimal point 8 places to the left, we get 4.56 and our power will be 8. So 456,000,000 becomes 4.56 x 10 8.
Feb 16­3:54 PM
Use Scientific Notation
Moving from scientific notation to standard numbers.
If you have a number written in scientific notation, you may be asked to write it as a standard number. A number such as 3.28 x 10 4 can be easily converted. All you have to do is move the decimal point to the right the number of spaces that is the same as the power that 10 is raised to. So for this number, you move your decimal point 4 spaces to the right, and you number is 32,800.
Scientific notation allows us to write very big or very small numbers in manner that is easy to read. When a number is written in scientific notation, it is made up of two parts. The left hand part is a number that is greater than or equal to one, but less than ten, and the right hand part is ten raised to a power. This power may be positive or negative. When the power is positive, the original number is greater than 1, and when the power is negative, the original number is less than one. For example, when we write 50,000 in scientific notation, it is written as 5 x 104. When we write .00008 in scientific notation, it is written as 8 x 10­5 .
Feb 16­3:54 PM
Use Scientific Notation
Small Numbers
For a small number such as 0.000005 we will be moving the decimal point to the right so that we have a number greater than or equal to one, but less than ten. The decimal point is moved 6 places to the right and this too is going to be the power we use with 10, and we have found a number between 1 and 10 and that number is 5. However when we move a decimal point to the right, the exponent will be negative. Since we have found our number between 1 and 10 and our power, we can now write 0.000005 in scientific notation as: 5 x 10­6
If we have a number such as 0.0000739 we use the same process. The decimal point is moved to the right until we get a number that is between 1 and 10. When we move our decimal point 5 places to the right, we get 7.39 and our power will be ­5. So 0.0000739 becomes 7.39 x 10 ­5.
Feb 16­3:54 PM
Use Scientific Notation
Rewrite in scientific notation.
587,000,000,000,000
The process is very similar when you have negative exponents. For 9.49 x 10 ­5 you move the decimal point 5 places to the left, and your number is 0.0000949
Feb 16­3:54 PM
Feb 16­3:54 PM
1
Algebra 1 CH 8.4 Use Scientific Notation.notebook
Use Scientific Notation
April 30, 2015
Use Scientific Notation
Rewrite in standard notation.
Rewrite in scientific notation.
7,254,000
Feb 16­3:54 PM
Use Scientific Notation
Rewrite in standard notation.
Feb 16­3:54 PM
Use Scientific Notation
Rewrite in scientific notation.
0.000,000,000,029
Feb 16­3:54 PM
Use Scientific Notation
Rewrite in scientific notation.
Feb 16­3:54 PM
Use Scientific Notation
Rewrite in standard notation.
0.000,000,147
Feb 16­3:54 PM
Feb 16­3:54 PM
2
Algebra 1 CH 8.4 Use Scientific Notation.notebook
Use Scientific Notation
Rewrite in standard notation.
Feb 16­3:54 PM
Use Scientific Notation
Multiply:
Feb 16­3:54 PM
Use Scientific Notation
Divide:
Feb 16­3:54 PM
April 30, 2015
Use Scientific Notation
Multiply:
Feb 16­3:54 PM
Use Scientific Notation
Multiply:
Feb 16­3:54 PM
Use Scientific Notation
Divide:
Feb 16­3:54 PM
3
Algebra 1 CH 8.4 Use Scientific Notation.notebook
April 30, 2015
Use Scientific Notation
Objective:Read and write numbers in scientific notation. Convert numbers from scientific notation to standard notation and vice versa. Multiply and divide numbers in scientific notation.
Feb 16­3:54 PM
4