Irrational numbers are numbers that cannot be expressed as a simple fraction. Their decimal representations go on forever without repeating. Approximating them means finding a rational number that is close to the irrational number. This is useful because it allows us to work with irrational numbers in practical calculations. For example, $\sqrt{2}$ is an irrational number, but we can approximate it as 1.414.
To approximate an irrational number, you can use methods like finding perfect squares around the number or using a calculator to get a decimal approximation and then rounding that decimal to a certain number of places. This worksheet will give you practice with both!
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Irrational Number | A. A number that can be expressed as a fraction $\frac{p}{q}$, where p and q are integers and q ≠ 0. |
| 2. Rational Number | B. The process of finding a value that is close to the exact value. |
| 3. Approximation | C. A number that cannot be expressed as a fraction; its decimal representation is non-repeating and non-terminating. |
| 4. Decimal Representation | D. A method of writing numbers that uses place value based on powers of 10. |
| 5. Perfect Square | E. The result of squaring a whole number (e.g., 9 is a perfect square because $3^2 = 9$). |
Complete the following sentences using the words provided: rational, irrational, approximation, decimal, square root.
An __________ number cannot be written as a simple fraction. Finding a close value is called an __________. A __________ number can be written as a fraction. The __________ representation of an irrational number never ends or repeats. Finding the __________ of a number is the opposite of squaring it.
Explain why approximating irrational numbers is useful in real-world situations. Give at least two specific examples.
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