Question

Make the following conversions using dimensional analysis. SHOW YOUR WORK. Express your answers in scientific notation.

Answer 1

(A) 14.8 g → 1.48 × 10^7 µg

The prefix µ means “× 10^(-6)”, so 1 µg = 1 × 10^(-6) g

The conversion factor (CF) = 1 µ g/1 × 10^(-6) g

∴ Mass = 14.8 g × [1 µg/1 × 10^(-6) g] = 1.48 × 10^7 µg

(B) 3.72 g → 3.72× 10^(-3) kg

The prefix k means “× 10^3”, so 1 kg = 1 × 10^3 g

CF = 1 kg/1 × 10^3 g

∴ Mass = 3.72 g × [1 kg/1 × 10^3 g] = 3.72× 10^(-3) kg

(C) 7.5 × 10^4 J →  75 kJ

CF = 1 kJ/1 × 10^3 J

∴ Energy = 7.5 × 10^4 J × [1 kJ/1 × 10^3 J] = 3.72× 10^(-3) kJ = 7.5 × 10^1 kJ

= 75 kJ