Here’s a structured overview based on your request regarding scientific notation and related concepts:
Vocabulary and Key Terms:
1. Coefficient
- Example: 5 in the expression \(5 \times 10^3\)
- Meaning: The numerical factor in a term, usually a number between 1 and 10, that is multiplied by a base raised to an exponent in scientific notation.
2. Base
- Example: 10 in the expression \(5 \times 10^3\)
- Meaning: The number that is raised to the exponent; in scientific notation, it is usually the number 10.
3. Exponent
- Example: 3 in the expression \(5 \times 10^3\)
- Meaning: The power to which the base is raised; it indicates how many times the base is multiplied by itself.
4. Scientific Notation
- Example: \(4.5 \times 10^6\)
- Meaning: A method of expressing numbers as a product of a coefficient (1 ≤ coefficient < 10) and a power of ten.
U4 L2
Example of a Large Number
- Example: 1,000,000 expressed as \(1 \times 10^6\)
Example of a Small Number
- Example: 0.0001 expressed as \(1 \times 10^{-4}\)
How to Compare Numbers in Scientific Notation
- Meaning: To compare, first compare the exponents. The number with the larger exponent is greater. If the exponents are the same, compare the coefficients.
U4 L3
Why Use Scientific Notation?
- Meaning: Scientific notation simplifies calculations with very large or very small numbers and makes them easier to read and understand.
What is this notation on the calculator: 1.388e-2?
- Meaning: This represents \(1.388 \times 10^{-2}\), which equals 0.01388.
U4 L4
List the Inequality Symbols and Their Meanings
- < (Less than): Indicates that the number on the left is smaller than the number on the right.
- > (Greater than): Indicates that the number on the left is larger than the number on the right.
- ≤ (Less than or equal to): Indicates that the number on the left is either smaller than or equal to the number on the right.
- ≥ (Greater than or equal to): Indicates that the number on the left is either larger than or equal to the number on the right.
U4 L5
Metric System and Powers of 10
- Meaning: The metric system uses powers of 10 as the basis for measurement; for example, 1 kilometer = \(10^3\) meters.
US Measures and Common Conversions
- Examples:
- 1 inch = 2.54 cm
- 1 foot = 0.3048 meters
- 1 mile = 1.60934 kilometers
U4 L6
What must be true for situations that involve adding and subtracting?
- Fractions: The denominators must be the same.
- Expressions: Like terms must be combined.
- Scientific Notation: The exponents must be the same before adding or subtracting the coefficients.
List the Steps for Add/Sub in SN
- Ensure the exponents are the same.
- Adjust the coefficients as needed.
- Add or subtract the coefficients.
- Write the result in scientific notation, adjusting the coefficient and exponent as necessary.
U4 L7
List the Words that Tell You to Add or Subtract
- Add: sum, more, increase, total, together
- Subtract: difference, less, decrease, remaining
U4 L8
Multiplication Exponent Rule Applied to SN
- When multiplying numbers in scientific notation, multiply the coefficients and add the exponents:
\( (a \times 10^m) \times (b \times 10^n) = (a \cdot b) \times 10^{(m+n)} \)
Words that Tell You to Multiply
- Multiply, times, product, times as many, of
U4 L9
Why is “how many times larger” a division problem?
- Meaning: To determine how many times one value is larger than another, you divide the larger number by the smaller number.
Words that Tell You to Divide
- Divide, ratio, per, out of, over
U4 L10
Name Some Situations that You Would Want to Use SN to Solve the Problem
-
Large Number Situations:
- Distances in astronomy (e.g., distance to stars)
- Population counts (e.g., global population)
- Economics (e.g., national debt)
-
Small Number Situations:
- Measurements in chemistry (e.g., concentrations of solutions)
- Sizes of bacteria or viruses
- Physics calculations involving precision (e.g., the mass of subatomic particles)
This format should provide a clear overview of the relevant topics related to scientific notation as per your request.