The symbol for approximately equal is known as the “approximately” symbol. In mathematics, it is normally written as two parallel wavy lines: ≈. A single tilde (~) has related but context-dependent meanings and is a different character.
In mathematics, the “approximately” symbol (which looks like the letter “≈”) communicates that two values are nearly but not exactly equal. The value on one side of the symbol is close enough to the value on the other side that they’re essentially interchangeable, though the values aren’t mathematically identical. In many cases, this happens when an expression’s result cannot be expressed as an exact number — for example, when you divide numbers that don’t divide evenly into each other.
You can think of this concept in terms of rounding. When you round off a number, such as π (pi), which is approximately 3.14, you’re effectively saying that the actual value is close enough to the rounded-off value that any practical use will see little difference between the two.
When to Use the Approximately Symbol
The key here is that the two values need to be close enough for the precision required by the context. For instance, if I told you that π is approximately 3.14, that is a standard two-decimal approximation. If someone else used 3.15, the difference might be acceptable for a rough estimate but not for a calculation that requires two correctly rounded decimal places. The symbol itself does not define the tolerance; the problem does.
Another way to think about this is how we express irrational quantities such as square roots. √2 is irrational, meaning its decimal expansion never ends nor repeats. This means that √2 cannot be expressed as a fraction with integers as numerator and denominator. Instead, we have to use an approximation, like √2 ≈ 1.414.
This also makes sense if you’re working with very small decimals that you’d prefer to work with, such as 0.999876 instead of 0.999876123468… There’s just no reason to deal with more decimals than necessary.
Other Symbols That Mean Approximately Equal
There are three symbols that mean approximately equal:
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≈: approximately equal to
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~: similar to
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≅: congruent to
These are distinct from one another and shouldn’t be used interchangeably. Here’s what they all mean:
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≈: This is the standard symbol for approximately equal to, and appears as two wavy lines between two numbers, variables, expressions, etc.
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~: This is often used in geometry to indicate similarity, which describes the relationship between figures that share the same shape but may differ in size. This might include things like triangles that have equal angles and proportional sides.
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≅: Like the “~” symbol, this is commonly used in geometry, too, to indicate congruence — that two figures are exactly the same in every way, including angle and length measurements.
While these signs do indicate different kinds of comparison, these symbols should not be used interchangeably.