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The **approximation symbol** $$\approx$$ is used to indicate that two values are close to each other but not exactly equal. It is read as "approximately." This symbol appears in mathematics whenever an exact value is replaced by a nearby rounded or estimated value. For example, $$\sqrt{5} \approx 2.24$$ states that the square root of $$5$$ is approximately $$2.24$$ — the two sides are close in value, but $$2.24$$ is not the exact square root of $$5$$. The approximation symbol differs from the equal sign ($$=$$), which asserts that two quantities have exactly the same value. Using $$\approx$$ instead of $$=$$ signals that some precision has been sacrificed, typically through rounding or truncating a decimal.

Approximation Symbol ($$\approx$$)

In a budget summary, a department head rounds an exact project cost of $24,991.15 to $25,000 to make the figure more manageable for an executive presentation. To show that these two values are close but not exactly equal, the head uses the symbol ≈. What is the formal name of this symbol, and how is it read when communicating the data verbally in a meeting?

Professional Notation for Rounded Budget Estimates

Define the mathematical symbol $\approx$ and state the specific rule for when this symbol should be used instead of the equal sign ($=$) in a professional or technical report. Provide one example of a statement using this symbol to show the relationship between a precise measurement and its rounded version.

Defining the Approximation Symbol in Professional Reports

Put the steps for using $$\approx$$ in the correct order.

How do you read the symbol $$\approx$$?

Which symbol means “approximately equal to”?

The symbol $$\approx$$ is called the _____ symbol.

What does $$\approx$$ mean?

Match each algebra term to its meaning.

Case context:
A calculator result is written as $$\sqrt{5} \approx 2.24$$.

Question:
What is the name of the symbol $$\approx$$, and what does it mean here?

Sample answer:
The symbol $$\approx$$ is the approximation symbol, read as “approximately.” It means $$2.24$$ is close to $$\sqrt{5}$$ but is not exactly equal to it.

Key points:
- $$\approx$$ is the approximation symbol.
- It is read as “approximately.”
- The values are close but not exactly equal.

Rubric:
The answer must name the approximation symbol and explain that the values are close but not exactly equal.

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