🔢 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, engineering, and mathematics. A number in scientific notation is written as $a \times 10^b$, where $a$ is a number between 1 and 10 (including 1 but excluding 10), and $b$ is an integer (positive or negative).
Converting from standard form to scientific notation involves moving the decimal point until there is only one non-zero digit to the left of it. The number of places you move the decimal determines the exponent of 10. If you move the decimal to the left, the exponent is positive; if you move it to the right, the exponent is negative.
🧠 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 method of writing very large or very small numbers |
| 3. Standard Form |
C. A number between 1 and 10 used in scientific notation |
| 4. Coefficient |
D. The usual way we write numbers |
| 5. Power of 10 |
E. 10 raised to an integer exponent |
(Answers: 1-B, 2-A, 3-D, 4-C, 5-E)
✍️ Part B: Fill in the Blanks
Complete the following sentences:
To write a number in scientific notation, you need a ______ and a ______ . The coefficient must be between ______ and ______. If you move the decimal to the left when converting from standard form, the exponent will be ______.
(Answers: coefficient, power of 10, 1, 10, positive)
🤔 Part C: Critical Thinking
Explain why scientific notation is useful for scientists and engineers. Give at least two reasons.