Represent each of the following combinations ~f units in the correct SI form using an appropriate prefix: (a) m/ ms,
(b) µkm,
(c) ks/ mg,
(d) km· µN.

(a) km/s

(b) mm

(c) Gs/kg

(d) mmN

Explanation:

(a) Given:

m / ms => the proper SI unit should be m/s

So let's convert to m/s

m / ms =

The denominator is ms which means milliseconds.

But milli = 10⁻³

∴ = =

Also 10³ = kilo (k)

=

∴ m / ms = =  km/s

(b) Given:

μkm => the proper SI unit should be m

So let's convert to m

μkm = 10⁻⁶ km [since μ = 10⁻⁶]

=> μkm = 10⁻⁶ x 10³ m [since k = 10³]

=> μkm = 10⁻³ m

But 10⁻³ = milli (m)

=> μkm = 10⁻³ m = mm

∴ μkm = mm

(c) Given:

ks/mg => the proper SI unit should be s/kg

So let's convert to s/kg

ks/mg = 10³s / mg [since k = 10³]

=> ks/mg = 10³s / 10⁻³g [since m = 10⁻³]

=> ks/mg = 10³ x 10³ s / g

=> ks/mg = 10⁶ s / g

=> ks/mg =

Multiply the numerator and denominator by 10³

=> ks/mg =

=> ks/mg =

=> ks/mg =  [since 10⁹ = Giga (G) ]

=> ks/mg =  [since 10³ = Kilo (k) ]

∴ ks/mg =  = Gs/kg

(d) Given:

km.μN => the proper SI unit should be mN or Nm

So let's convert to km.μN

km.μN = 10³m.μN                 [since k = 10³]

=> km.μN = 10³m.10⁻⁶N        [since μ = 10⁻⁶]

=> km.μN = 10⁻³ mN

=> km.μN = mmN             [since m = milli = 10⁻³]

∴ km.μN = mmN

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