Perform each of the following conversions using metric conversion factors a) 44.2 mL to Liters b) 8.65 m to nanometers c) 5.2 x 10^8 g to megagrams
The Correct Answer and Explanation is:
Let’s go through each of the conversions step-by-step:
a) 44.2 mL to Liters
To convert milliliters (mL) to liters (L), we use the conversion factor:1 L=1000 mL1 \, \text{L} = 1000 \, \text{mL}1L=1000mL
This means that 1 liter is equivalent to 1000 milliliters. Therefore, to convert 44.2 mL to liters, we divide by 1000:44.2 mL×1 L1000 mL=0.0442 L44.2 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.0442 \, \text{L}44.2mL×1000mL1L=0.0442L
So, 44.2 mL = 0.0442 L.
b) 8.65 m to Nanometers
To convert meters (m) to nanometers (nm), we use the conversion factor:1 m=109 nm1 \, \text{m} = 10^9 \, \text{nm}1m=109nm
This means that 1 meter is equivalent to 1 billion nanometers. To convert 8.65 meters to nanometers, we multiply by 10910^9109:8.65 m×109 nm/m=8.65×109 nm8.65 \, \text{m} \times 10^9 \, \text{nm/m} = 8.65 \times 10^9 \, \text{nm}8.65m×109nm/m=8.65×109nm
So, 8.65 m = 8.65 × 10^9 nm.
c) 5.2 x 10^8 g to Megagrams
To convert grams (g) to megagrams (Mg), we use the conversion factor:1 Mg=106 g1 \, \text{Mg} = 10^6 \, \text{g}1Mg=106g
This means that 1 megagram is equal to 1 million grams. To convert 5.2×1085.2 \times 10^85.2×108 grams to megagrams, we divide by 10610^6106:5.2×108 g×1 Mg106 g=5.2×102 Mg5.2 \times 10^8 \, \text{g} \times \frac{1 \, \text{Mg}}{10^6 \, \text{g}} = 5.2 \times 10^2 \, \text{Mg}5.2×108g×106g1Mg=5.2×102Mg
So, 5.2 × 10^8 g = 520 Mg.
In summary:
- 44.2 mL = 0.0442 L
- 8.65 m = 8.65 × 10^9 nm
- 5.2 × 10^8 g = 520 Mg
These conversions are done by applying the appropriate conversion factors between metric units. It’s important to understand that the metric system is based on powers of 10, which simplifies the conversion process.
