Question

dimensional analysis
use dimensional analysis for each of the following problems:

1. how many cm³ are equal to 14.6 ml?

1. how many kilograms are equal to 1.5 × 10⁵ mg?

1. how many miles are equal to 1.7 km? (1 inch = 2.54 cm)

1. how many seconds are in the month of june? (30 days)

1. the density of aluminum is 2.70 g/dl. what is this density in lb/ml? (1 oz = 28.34 g)

Explanation:

Step1: Convert m to cm

$14.6\ \text{m} \times \frac{100\ \text{cm}}{1\ \text{m}} = 1460\ \text{cm}$

Step2: Convert mg to kg

$1.5 \times 10^7\ \text{mg} \times \frac{1\ \text{g}}{1000\ \text{mg}} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 15\ \text{kg}$

Step3: Convert km to miles

$1.7\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{100\ \text{cm}}{1\ \text{m}} \times \frac{1\ \text{inch}}{2.54\ \text{cm}} \times \frac{1\ \text{mile}}{63360\ \text{inches}} \approx 1.056\ \text{miles}$

Step4: Convert June to seconds

$30\ \text{days} \times \frac{24\ \text{hrs}}{1\ \text{day}} \times \frac{60\ \text{min}}{1\ \text{hr}} \times \frac{60\ \text{sec}}{1\ \text{min}} = 2592000\ \text{seconds}$

Step5: Convert g/dL to lb/mL

$2.70\ \frac{\text{g}}{\text{dL}} \times \frac{1\ \text{oz}}{28.34\ \text{g}} \times \frac{1\ \text{lb}}{16\ \text{oz}} \times \frac{1\ \text{dL}}{100\ \text{mL}} \approx 5.95 \times 10^{-5}\ \frac{\text{lb}}{\text{mL}}$

Answer:

1. $1460\ \text{cm}$
2. $15\ \text{kg}$
3. $\approx 1.06\ \text{miles}$ (rounded to 2 decimal places)
4. $2592000\ \text{seconds}$
5. $\approx 5.95 \times 10^{-5}\ \frac{\text{lb}}{\text{mL}}$