Question

Convert using dimensional analysis step by step:

a) 35kg to g
b) 7.2cm^2 to m^2
c) 81m^3 to km^3
d) 24.9 MJ to cJ
e) 27.31 km/hr to m/s

Answer 1

Set these up in a way where the units will reduce out. You will multiply by the factor(s) needed to go from one unit to the other.

a)
`35 kg * (1000g)/(1kg) = 35000 g`

b)
`7.2cm^2 * (1m * 1m)/(100cm * 100cm) = 7.2 * 10^(-4) m^2`

c)
`81m^3 * (1km * 1km * 1km)/(1000m * 1000m * 1000km) = 8.1 * 10^(-8) km^3`

d)
`24.9Mj * (10^8cJ)/(1Mj) = 24.9 * 10^8 cJ`

e)
`27.31 km/hr * (1000m)/(1km) * (1hr)/(3600s) = 7.59m/s`