4 Scientific Notation

Vocabulary
Key Terms
Meaning/Definition/Picture
Example
U4 L1
Coefficient

U4 L1
Base

Exponent

U4 L1
Scientific Notation

U4 L2
Example of large number

Example of small number

U4 L2
How to compare numbers in Scientific Notation

U4 L3
Why use Scientific Notation?

U4 L3
What is this notation on the calculator:
1.388e-2?

U4 L4
List the inequality symbols and their meaning

U4 L5
Metric system and powers of 10

U4 L5
US measures and common conversions

U4 L6
What must be true for situations that involve adding and subtracting?
Fractions

Expressions

Scientific Notation

U4 L6
List the steps for Add/Subt in SN

U4 L7
List the words that tell you to add or subtract
Add

Subtract

U4 L8
Multiplication Exponent Rule applied to SN

U4 L8
Words that tell you to multiply

U4 L9
Why is “how many times larger” a division problem?

U4 L9
Words that tell you to divide

U4 L10
Name some situations that you would want to use SN to solve the problem.
Large Number situations:

Small Number situations:

1 answer

Here's a filled-out table for the vocabulary related to scientific notation, including definitions and examples.

4 Scientific Notation

| Key Terms | Meaning/Definition/Picture | Example | |----------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------| | U4 L1 Coefficient | The number that is multiplied by the power of ten in scientific notation, must be greater than or equal to 1 and less than 10. | 3.5 × 10² (here, 3.5 is the coefficient) | | U4 L1 Base | The number that is being raised to a power, in scientific notation, the base is always 10. | 10 in 3.5 × 10² | | U4 L1 Exponent | The power to which the base is raised, indicating the number of times the base is multiplied by itself. | 2 in 3.5 × 10² | | U4 L1 Scientific Notation | A method of expressing numbers that are too large or too small to be conveniently written in decimal form, using powers of ten. | 6.02 × 10²³ (Avogadro's number) | | U4 L2 Example of large number | An example of a large number in scientific notation. | 1.0 × 10⁶ (1 million) | | U4 L2 Example of small number | An example of a small number in scientific notation. | 2.5 × 10⁻³ (0.0025) | | U4 L2 How to compare numbers in Scientific Notation | Compare the exponents first; if they are the same, compare the coefficients. | 2.1 × 10³ vs. 1.9 × 10⁴ → Compare 3 vs 4 to see 2.1 × 10³ is smaller. | | U4 L3 Why use Scientific Notation? | It simplifies calculations with very large or very small numbers and makes them easier to read and write. | Calculating distances in space. | | U4 L3 What is this notation on the calculator: 1.388e-2? | This means 1.388 × 10⁻², which is another way to express 0.01388. | 1.388e-2 = 0.01388 | | U4 L4 List the inequality symbols and their meaning | < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), = (equal). | e.g., 2 < 3, 5 ≥ 5 | | U4 L5 Metric system and powers of 10 | The metric system is based on powers of 10; prefixes denote the size of the measurement (e.g., kilo- = 10³, milli- = 10⁻³). | 1 kilometer = 10³ meters | | U4 L5 US measures and common conversions | Common conversions include inches to centimeters (1 inch = 2.54 cm), pounds to kilograms (1 lb = 0.453592 kg). | Convert 5 feet to cm: 5 × 30.48 = 152.4 cm | | U4 L6 What must be true for situations that involve adding and subtracting? Fractions, Expressions, Scientific Notation | The numbers must have the same exponent when adding or subtracting in scientific notation. | 2.0 × 10² + 3.0 × 10² = 5.0 × 10² | | U4 L6 List the steps for Add/Subt in SN| 1. Adjust the numbers to have the same exponent. 2. Add or subtract the coefficients. 3. Combine and express the result in scientific notation if needed. | 2.0 × 10² + 3.0 × 10² = 5.0 × 10²| | U4 L7 List the words that tell you to add or subtract | Add: plus, sum, increased by, combined with; Subtract: minus, difference, decreased by, less than. | e.g., "What is 5 increased by 3?"| | U4 L8 Multiplication Exponent Rule applied to SN| When multiplying numbers in scientific notation, multiply the coefficients and add the exponents. | (2 × 10²) × (3 × 10³) = 6.0 × 10⁵ | | U4 L8 Words that tell you to multiply | Multiply: product, times, of, as much as, each, combined. | e.g., "5 times 3" | | U4 L9 Why is “how many times larger” a division problem? | It compares two quantities and involves finding out how many times one value fits into another, requiring division. | e.g., "How many times larger is 50 than 5?" | | U4 L9 Words that tell you to divide | Divide: quotient, per, ratio, out of, shared among. | e.g., "Divide 10 by 2" | | U4 L10 Name some situations that you would want to use SN to solve the problem. | Large Number situations: astronomy (distances between stars), population sizes; Small Number situations: atomic sizes, quantities in chemistry. | Large: Distance to stars; Small: Size of a virus. |

This should cover the vocabulary and examples for each section related to scientific notation!