College Algebra: Section 1.2b (Packet #4)
By the end of the section, you should be able to:
- Convert a number from standard form into scientific notation
- Convert a number in scientific notation into standard form.
- Use the properties of exponents to solve problem only using scientific notation.
- Solve surface area and volume problems using basic geometric formulas
Definitions:
- Standard Notation: How we are used to seeing numbers, each digit represents a tens place.
- Standard notation is hard to read and cumbersome to use when working with really large or really small numbers.
- Scientific Notation: A method of writing a number in terms of a decimal number between 1 and 10, multiplied by a power of 10.
- This is a convenient way to work with large numbers as it typically makes the number shorter by avoiding the use of some zeros as placeholders.
Converting Numbers to/from Scientific Notation
🎥Examples 1&2
🎥Examples 1&2
Examples of Using Properties of Exponents to Simplify Scientific Notation Expressions
🎥Examples 3&4
*Note that there is a mistake in the video on Example 4. 34-12 should be 22 for the exponent rather than 21, the overall answer will be 3.5x10^29
🎥Examples 3&4
*Note that there is a mistake in the video on Example 4. 34-12 should be 22 for the exponent rather than 21, the overall answer will be 3.5x10^29
Things to remember about scientific notation:
- There can only be one digit to the left of the decimal place.
- This digit can only be between 1 and 10. The number must be less than 10, but it can be equal to 1.
- When converting from scientific notation to standard form.
- 10 to the power of a POSTIVE number makes the decimal number BIGGER. (Ex. 1)
- 10 to the power of a NEGATIVE number make the decimal number SMALLER. (Ex. 2)
- When solving using properties of exponents, separate the decimal numbers and the powers of 10. Use basic multiplication/division to combine the decimal numbers and use the properties of exponents to simplify the powers of 10.
- If a number is greater than 10,000 or smaller than 0.0001, it should typically be written in scientific notation.
Basic Geometric Formulas
** These formulas should be memorized
** These formulas should be memorized
Examples of finding surface area/volume using basic Geometric Figures
🎥Examples 5&6
🎥Examples 5&6
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