📚 Topic Summary
Scientific notation is a way to express very large or very small numbers in a compact form. It's written as $a \times 10^b$, where 'a' is a number between 1 and 10 (but not including 10), and 'b' is an integer (a positive or negative whole number). When converting large numbers to scientific notation, you're essentially moving the decimal point until you have a number between 1 and 10 and then counting how many places you moved the decimal. That count becomes your exponent.
For example, the number 5,000,000 can be written in scientific notation as $5 \times 10^6$. This makes it easier to work with these numbers, especially in calculations.
🧮 Part A: Vocabulary
Match the terms on the left with their definitions on the right:
| Term |
Definition |
| 1. Scientific Notation |
A. The number that is multiplied by a power of 10 in scientific notation. |
| 2. Exponent |
B. The number of times 10 is multiplied by itself in scientific notation. |
| 3. Coefficient |
C. A method of writing very large or very small numbers in a compact form. |
| 4. Power of 10 |
D. A number expressed as 10 raised to an exponent. |
| 5. Standard Form |
E. The usual way of writing numbers, without using exponents. |
Match the following: 1-C, 2-B, 3-A, 4-D, 5-E
📝 Part B: Fill in the Blanks
Complete the following paragraph using the words provided: exponent, scientific notation, decimal point, large number, power of 10.
When converting a ________________ to ________________, you move the ________________ until you have a number between 1 and 10. The number of places you moved the ________________ becomes the ________________ in the ________________.
Answer: large number, scientific notation, decimal point, decimal point, exponent, power of 10
🤔 Part C: Critical Thinking
Explain why scientific notation is useful for representing very large numbers. Give at least two real-world examples where it is commonly used.