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) $35 kg \times \frac{1000g}{1kg} = 35000 g$

b) $7.2cm^2 \times \frac{1m \times 1m}{100cm \times 100cm} = 7.2 \times 10^{-4} m^2$

c) $81m^3 \times \frac{1km \times 1km \times 1km}{1000m \times 1000m \times 1000km} = 8.1 \times 10^{-8} km^3$

d) $24.9Mj \times \frac{10^8cJ}{1Mj} = 24.9 \times 10^8 cJ$

e) $27.31 km/hr \times \frac{1000m}{1km} \times \frac{1hr}{3600s} = 7.59m/s$