📚 Topic Summary
In math, especially when dealing with circles, we often encounter $\pi$ (pi). Pi is an irrational number, meaning its decimal representation goes on forever without repeating. Because of this, we usually use approximations like 3.14 or $\frac{22}{7}$. An exact answer keeps $\pi$ as $\pi$ in the answer. An approximate answer replaces $\pi$ with a decimal or fraction to get a numerical value.
For example, if the radius of a circle is 5, the area is exactly $25\pi$. An approximate answer would be $25 \times 3.14 = 78.5$
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Exact Answer |
A. A number that cannot be expressed as a simple fraction. Its decimal representation neither terminates nor repeats. |
| 2. Approximate Answer |
B. A value that is close to the true value but not precisely accurate. |
| 3. Pi ($\pi$) |
C. An answer that includes $\pi$ and is not rounded to a decimal value. |
| 4. Radius |
D. The distance from the center of a circle to any point on its circumference. |
| 5. Irrational Number |
E. The ratio of a circle's circumference to its diameter, approximately 3.14159. |
✏️ Part B: Fill in the Blanks
Fill in the missing words in the paragraph below:
When calculating the area of a circle, the formula is $A = \pi r^2$, where 'r' represents the _________. If you want an _________ answer, you will substitute a numerical value like 3.14 for _________. However, if you want an _________ answer, you'll leave your answer in terms of _________. Leaving the answer in terms of pi gives a more _________ representation.
🤔 Part C: Critical Thinking
Explain why it's sometimes useful to give an approximate answer instead of an exact answer, even though the exact answer is more accurate. Provide an example.