📚 Topic Summary
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in standard decimal form. It is commonly used in science and engineering. A number in scientific notation is written as the product of two numbers: a coefficient (a number between 1 and 10) and a power of 10. Converting between scientific notation and standard notation involves moving the decimal point to the right or left, depending on whether the exponent of 10 is positive or negative.
For example, the number 3,000,000 can be written in scientific notation as $3 \times 10^6$, and the number 0.000045 can be written as $4.5 \times 10^{-5}$. Understanding how to convert between these forms is fundamental to many calculations and measurements.
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Coefficient |
A. The standard way of writing numbers. |
| 2. Exponent |
B. A method of writing very large or very small numbers using powers of 10. |
| 3. Scientific Notation |
C. The number that indicates the power to which 10 is raised. |
| 4. Standard Notation |
D. The number between 1 and 10 in scientific notation. |
| 5. Power of 10 |
E. 10 raised to a certain exponent. |
(Answers: 1-D, 2-C, 3-B, 4-A, 5-E)
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided:
(exponent, coefficient, standard, scientific notation, decimal)
To convert a number from __________ notation to __________ notation, you need to adjust the position of the __________ point based on the __________. The __________ must be a number between 1 and 10.
(Answers: standard, scientific notation, decimal, exponent, coefficient)
🤔 Part C: Critical Thinking
Explain why scientific notation is useful in fields like astronomy. Provide an example.