One bar is exactly 100,000 pascals. The round number is the whole reason the bar exists: the pascal is too small to be convenient for most real pressures, and multiplying by a hundred thousand is easier than remembering an arbitrary constant.
About the units
The pascal is the SI derived unit of pressure, defined as one newton per square metre, and named after Blaise Pascal, whose experiments in the 1640s established that atmospheric pressure decreases with altitude. It is a very small unit in human terms: a sheet of paper resting on a table exerts about one pascal. Atmospheric pressure is 101,325 Pa, a car tyre around 250,000 Pa, and a diving cylinder 20,000,000 Pa. The bar was created to make those numbers manageable without abandoning the metric system, and although SI discourages it, it is entrenched in engineering, meteorology and diving.
The exact factor
The factor is exactly 100,000, or 10⁵. The prefixed forms line up neatly as a result: 1 bar = 100 kPa = 0.1 MPa, and 1 millibar = 100 Pa = 1 hectopascal. That last identity is why meteorologists could switch from millibars to hectopascals in the 1980s without changing a single number on a weather chart. For very low pressures the microbar appears in acoustics, equal to 0.1 Pa, and it is the reference against which older sound pressure levels were quoted.
Where you meet this conversion
Engineering documentation that must be SI-compliant states pressures in pascals or their prefixed forms while the equipment itself is marked in bar, so the conversion appears in nearly every specification review. Finite element analysis and fluid dynamics software works in pascals internally. Building services, ventilation and cleanroom differential pressures are quoted in pascals because the quantities are genuinely small — a cleanroom might be held 15 Pa above ambient.