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Scientific Notation. Making large and small numbers more manageable. Scientific notation is a system for representing a number as a number between 1 and 10 multiplied by a power 10. - PowerPoint PPT Presentation
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Scientific Notation
Making large and small numbers more manageable.
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
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
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
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
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
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
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
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
Practice Questions:
74,390,000 = __________ x 10_
0.000009998 = _________ x 10_
-0.0000623 = __________ x 10_
5.466 x 106 = __________
2.3 x 10-4 = ___________
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 = ___________
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 = ___________
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 = ___________
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 = __________
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__
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.
Concept Question
• How would you express a number such as 1.5 or 0.2 in scientific notation?