10.0 Units Conversion Tips
[10.1] Units calculations are approximate in Auto mode
Bhuvanesh reports:
When in AUTO or APPROX mode, the units system works in approximate mode. So, for example,
9*_dollars/_hour*8*_hour/_day*5*_day/_week*12*_week/_summer
returns
4320.0000000002*(_dollars/_summer)
Note that exact(ans()) still returns this answer. If this calculation is performed in EXACT mode, it
returns
4320.*(_dollars/_summer)
Notice that it keeps the decimal point, even in EXACT mode.
(credit to Bhuvanesh Bhatt)
[10.2] Convert compound units to equivalent units
In some cases, you can use the built-in units conversion to express some units in terms of base units.
Some examples:
_coul▶_s 1·_A·1·_s
_J▶_N 1·_m·1·_N
_F▶1/_V 1·_coul/1·_V
_W▶1/_s 1·_J/1·_s
_henry▶1/_s (1·_kg·1·m²) / (1·_A·1·_coul·1·_s)
_Wb▶1/_A 1·_J / 1·_A
If the converted-to unit appears in the denominator of the result, you need to express that unit as a
reciprocal in the conversion command.
This method does not necessarily return the converted unit in terms of base units. This can be seen in
the third example above, in which capacitance in farads (F) is converted to coulomb/volt. Neither the
coulomb nor the volt are bases units; a true base-units conversion would be (A
2
*s
4
)/(kg*m
2
). For
reference, the seven SI base system units are:
Length, meter (m) Temperature, degrees Kelvin (K)
Mass, kilogram (kg) Luminous intensity, candela (cd)
Time, second (s) Amount of substance, mole (mol)
Electric current, amp (A)
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