Scientific Notation

1. Scientific Notation Making large and small numbers more manageable.

2. Scientific notation is a system for representing a number as a number between 1 and 10 multiplied by a power 10. Scientific nation is most useful for presenting very large or very small numbers in a form that is easier to use. For example: The sets of numbers below are equivalent. However, the numbers of the right can be read much more easily. 253,000,000,000,000,000,000 = 2.53 x 1020 0.0000000000000000000253 = 2.53 x 10-20

3. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. 120.3 = 1.203 x 100 100 is the same as 102

4. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. 120.3 = 1.203 x 102 100 is the same as 102

5. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. 1203 = 1.203 x 1000 1000 is the same as 103

6. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. 1203 = 1.203 x 103 1000 is the same as 103

7. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. 0.1203 = 1.203 x 10-1 1/10 is the same as 10-1

8. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. An easy way to determine the exponent of ten is to count the decimal positions you move. 0.000001203 = 1.203 x 10-6 The decimal has moved backwards: 6 position

9. In scientific notation, numbers are expressed as a number between 1 and 10 multiplied by 10 raised to an exponent. An easy way to determine the exponent of ten is to count the decimal positions you move. 1203000000 = 1.203 x 109 The decimal has moved forwards: 9 positions

10. Practice Questions: 74,390,000 = __________ x 10_ 0.000009998 = _________ x 10_ -0.0000623 = __________ x 10_ 5.466 x 106 = __________ 2.3 x 10-4 = ___________

11. Practice Questions: 74,390,000 = ___7.439__ x 107 0.000009998 = _________ x 10_ -0.0000623 = __________ x 10_ 5.466 x 106 = __________ 2.3 x 10-4 = ___________

12. Practice Questions: 74,390,000 = ___7.439__ x 107 0.000009998 = _9.998___ x 10-6 -0.0000623 = __________ x 10__ 5.466 x 106 = __________ 2.3 x 10-4 = ___________

13. Practice Questions: 74,390,000 = ___7.439__ x 107 0.000009998 = _9.998___ x 10-6 -0.0000623 = ___-6.23___ x 10-5 5.466 x 106 = __________ 2.3 x 10-4 = ___________

14. Practice Questions: 74,390,000 = ___7.439__ x 107 0.000009998 = _9.998___ x 10-6 -0.0000623 = ___-6.23___ x 10-5 5.466 x 106 = __5466000_ 2.3 x 10-4 = __________

15. Practice Questions: 74,390,000 = ___7.439__ x 107 0.000009998 = _9.998___ x 10-6 -0.0000623 = ___-6.23___ x 10-5 5.466 x 106 = __5466000_ 2.3 x 10-4 = __0.00023__

16. Scientific notation makes it easier to express very large or very small numbers in more manageable terms. It is used widely in the scientific community when referencing everything from numbers of bacterial to concentrations of solution.

17. Concept Question • How would you express a number such as 1.5 or 0.2 in scientific notation?