Using the Approximately Equal Sign
The approximately equal sign is a pair of stacked tildes. It tells the reader that the two sides agree closely but not exactly, whether because a value has been rounded (√2 ≈ 1.414), estimated (the crowd was ≈ 5,000) or converted between units (1 inch ≈ 2.54 cm, though that one happens to be exact). It is the standard sign in physics, engineering and statistics for "close enough for this purpose".
One tilde or two?
The single tilde ~ on your keyboard is the informal ancestor. In hand-written notes and in code comments it is understood, and it is the only option in plain-ASCII contexts such as filenames and SMS. In typeset maths the single tilde operator ∼ has other meanings: X ∼ N(0, 1) says a variable follows a distribution, and A ∼ B says two matrices or triangles are similar. Using it for approximation in a paper invites misreading, so the double tilde ≈ is preferred whenever the font supports it, which today is everywhere.
≈, ≃ and ≅
The three signs look alike and are routinely mixed up. ≈ is numerical closeness. ≃ (tilde over one bar) marks asymptotic equality, meaning two functions grow at the same rate, and is also used for homotopy equivalence. ≅ (tilde over two bars) is congruence in geometry and isomorphism in algebra, a statement about structure rather than magnitude. If you are describing numbers, ≈ is always the one you want; the others say something stronger about shape or growth.
Spacing and position
Set it with a space on either side, exactly as you would the not equal sign: 22/7 ≈ 3.1429. When it prefixes a lone estimate it closes up, as in "≈40 minutes", mirroring the prefix use of ±. The glyph is centred on the maths axis, so its waves align with the bars of a neighbouring equals sign.
Typing
Mac users press Option + X. On Windows the Latin-1 Alt codes do not cover it, but the DOS-era Alt + 247 still works in many programs, and Word turns 2248 into ≈ after Alt + X. Phones are friendlier than for most maths symbols: on the iPhone, holding = on the #+= page reveals both ≈ and ≠, and Gboard does the same on most builds. In HTML the entity is ≈, and LaTeX uses \approx, with \simeq and \cong for the two look-alikes.
Casual and creative uses
Online, ≈ softens a number without a caveat sentence: "≈ 3 hrs of sleep", "reads ≈ 50 books a year". It also serves as a wavy divider in aesthetic symbols layouts, where its double wave complements ∼ and ≋ in ocean-themed bios. Because it is text rather than an emoji, it will not swap to a coloured icon on someone else's phone, and it is an easy way to add a scholarly touch to a caption styled with the italic fonts generator.