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!