๐ Topic Summary
Scientific notation is a way to express very large or very small numbers in a compact form. It is written as a number between 1 and 10 multiplied by a power of 10. For example, the number 3,000,000 can be written in scientific notation as $3 \times 10^6$. Converting to and from scientific notation involves moving the decimal point and adjusting the exponent of 10 accordingly. Scientific notation makes it easier to work with extreme values in science and engineering.
When converting a number to scientific notation, move the decimal point until there is only one non-zero digit to the left of it. The number of places you moved the decimal point becomes the exponent of 10. If you moved the decimal to the left, the exponent is positive; if you moved it to the right, the exponent is negative. Conversely, to convert from scientific notation to standard form, move the decimal point the number of places indicated by the exponent. Move it to the right for positive exponents and to the left for negative exponents.
๐ค Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Scientific Notation |
A. The number of times 10 is multiplied by itself. |
| 2. Exponent |
B. A way to express numbers as a product of a number between 1 and 10 and a power of 10. |
| 3. Coefficient |
C. The number between 1 and 10 in scientific notation. |
| 4. Standard Form |
D. A number written with all its digits, without using exponents. |
| 5. Power of 10 |
E. 10 raised to an exponent. |
Answers:
- ๐ 1 - B
- ๐ก 2 - A
- ๐ 3 - C
- ๐งช 4 - D
- ๐ 5 - E
โ๏ธ Part B: Fill in the Blanks
Fill in the missing words in the following paragraph:
__________ notation is a way of writing very large or small numbers. It uses a __________ multiplied by a power of __________. The exponent indicates how many places the decimal point is __________. A __________ exponent means the number is greater than 1, while a __________ exponent means the number is less than 1.
Answers: Scientific, coefficient, 10, moved, positive, negative
๐ค Part C: Critical Thinking
Why is scientific notation useful in fields like astronomy and microbiology?
Answer: Scientific notation is useful because it allows scientists to express extremely large distances (in astronomy) and extremely small sizes (in microbiology) in a manageable and easily comparable format. It simplifies calculations and makes numbers easier to work with.
