Express the following in `SI` unit:
a. `6'10"` b. `200 lb'`
c. `60 "miles" h^(-1)` d. `-20^(@)C`
e. `2.53 mm` f. `7.85 mL`
g. `0.0528 "in"` h. `52 mu g`
i. `5 "days"` j. `5 L`
k. `14 lb "in"^(-2)` (atmospheric pressure)
l. `6.86 g cm^(-3)` density of metal)

Explanation

a. `SI` unit of length is metre.
`1 ft = 12 "in"`
`:. 6' 10" = 12 xx 6 + 10 = 82"` or `82 "in"`
`:. 82 "in" = 82 "in" xx (2.54 cancel(cm))/(1 cancel("in")) xx (1 m)/(100 cancel(cm))`
`= 2.0828 m = 2.08 m`
`SI` unit of mass is `kg`.
`1 lb = 454 g`
`:. 200 lb = 200 lb xx (454 cancel(g))/(1 cancel(lb)) xx (1 kg)/(1000 cancel(g)) = 90.8 kg`
c. `SI` unit of speed is `m s^(-1)`.
`(60 "miles")/(1 "hour") = (60 "miles")/(3600 s) xx (1760 cancel(yd))/(1 cancel("miles")) xx (3 cancel(ft))/(1 cancel(yd))`
`xx (12 "in")/(1 cancel(ft)) xx (2.54 cancel(cm))/(1 cancel("in")) xx (1 m)/(100 cancel(cm))`
`= 26.82 m s^(-1) = 26.8 m s^(-1)`
`SI` unit of temperature in kelvin
`20^(@)C = - 20 + 273.15 K = 253.15 K`
e. `SI` unit of lenght is metre `(m)`.
`1 m = 100 cm, 1 cm = 10 mm`
unit conversion factors are:
`:. (1 m)/(100 cm) = 1 = (100 cm)/(1 m)`
and `(1 cm)/(10 mm) = 1 = (10 cm)/(1 cm)`
`:. 2.53 mm = 2.53 cancel(mm) xx (1 cancel(mm))/(10 cancel(mm)) xx (1 m)/(100 cancel(cm))`
`SI` unit of volume is `("metre")^(3)` or `m^(3)`
`7.85 mL = 7.85 cancel(mL) xx (1 cancel(cm^(3)))/(10 cancel(mL)) xx (1 m)/(100 cancel(cm))`
`xx (1 m)/(100 cancel(cm)) xx (1 m)/(100 cancel(cm))`
`= 7.85 xx 10^(-6) m^(3)`
g. `SI` unit of length is metre `(m)`.
`0.0528 "in" 0.0258 cancel("in") xx (2.54 cancel(cm))/(1 cancel(in)) xx (1 m)/(100 cancel(cm))`
`= 1.341 xx 10^(-3) m`
h. `SI` unit of mass is `'kg'`
and `1 mu g` (micro gram) `= 10^(6) g`
`52 mu g = 52 cancel(mu g) xx (10^(-6) cancel(g))/(1 cancel(mu g)) xx (1 kg)/(1000 cancel(g)) = 5.2 xx 10^(-8) kg`
i. `SI` unit of time is second `(s)`.
`:. 5 "days" = 5 cancel("days") xx (24 cancel(h))/(1 cancel("days")) xx (60 cancel("min"))/(1 cancel(h)) xx (60 s)/(1 cancel("min"))`
`= 5 xx 24 xx 60 xx 60 s = 432000 s`
j. `SI` unit of volume is `dm^(3)`.
`:. 5 L = 5 L xx (1000 cm^(3))/(1 L) xx (1 dm)/(10 cancel(cm)) xx (1 dm)/(10 cancel(cm)) xx (1 dm)/(10 cancel(cm))`
`= 5 dm^(3)`
k. `SI` unit of pressure is `kg m^(-2)` and `1 kg = 2.205 lb`.
`:. (14 lb)/(1 "in"^(2)) = (14 cancel(lb))/(1 cancel("in"^(2)) xx (1 kg)/(2.205 cancel(lb)) xx (1 cancel("in"))/(2.54 cancel(cm))`
`xx (1 cancel("in"))/(2.54 cancel(cm)) xx (100 cancel(cm))/(1 m) xx (100 cancel(cm))/(1 m)`
`= (14 x 100 xx 100)/(2.205 xx 2.54 xx 2.54)`
`= 9841.28 kg m^(-2)`
`= 9841.3 kg m^(-2)` (rounding off)
l. `SI` unit of desity is `kg m^(-3)`.
`(6.86 g)/(1 cm^(3)) = (6.86 cancel(g))/(1 cancel(cm^(3))) xx (1 kg)/(100 cancel(g)) xx (100 cancel(cm))/(1 m)`
`xx (100 cancel(cm))/(1 m) xx (100 cancel(cm))/(1 m)`
`= 6.86 xx (10^(6))/(10^(3)) = 6860 kg m^(-3)`