12 Questions
Which form is preferred by scientists for expressing numbers, regardless of their size?
Exponential form
What is the exponential form of the speed of light, which is 186,000 miles per second?
1.86 x 10^5
What is the ordinary form of the diameter of an E. coli cell, which is 8.0 x 10^-7 meters?
0.0000008 meters
Which form is useful for expressing very large or very small numbers?
Exponential form
Which form do scientists prefer to use for expressing numbers, regardless of their size?
Exponential form
What is the ordinary form of 1.86 x 10^5?
186,000
What is the ordinary form of 8.0 x 10^-7 meters?
0.00000080 meters
When an ordinary number smaller than one will have a positive exponent?
When the decimal point is moved to the left
What is the exponential form of 4.95 x 10^9?
4950000000
When an ordinary number larger than one will have a positive exponent?
When the decimal point is moved to the right
What is the exponential form of 5.6 x 10^-13?
0.00000000000056
How many places should the decimal point be moved to the right to convert an ordinary number smaller than one to exponential form?
Equal to the number of places the decimal point has been moved to the left
Study Notes
Scientific Notation
- Scientists prefer to express numbers in exponential form, regardless of their size, for simplicity and clarity.
Exponential Form
- The speed of light, 186,000 miles per second, can be written in exponential form as 1.86 x 10^5.
- The diameter of an E. coli cell, 8.0 x 10^-7 meters, is already in exponential form.
Ordinary Form
- The ordinary form of 1.86 x 10^5 is 186,000.
- The ordinary form of 8.0 x 10^-7 meters is 0.0000008 meters.
Characteristics of Exponential Form
- Exponential form is useful for expressing very large or very small numbers.
- Ordinary numbers smaller than one will have a negative exponent in exponential form.
- Ordinary numbers larger than one will have a positive exponent in exponential form.
- The exponential form of 4.95 x 10^9 is already in exponential form.
- The exponential form of 5.6 x 10^-13 is already in exponential form.
Converting to Exponential Form
- To convert an ordinary number smaller than one to exponential form, the decimal point should be moved to the right.
Test your knowledge of exponential and ordinary forms of numbers with this quiz! Explore the importance of exponential notation in scientific calculations and learn how to convert between the two forms. Challenge yourself with examples of both large and small numbers.
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