Dimensional Analysis & Unit Conversions

To convert liters to milliliters, you multiply the volume in liters by 1,000, since 1 liter equals 1,000 milliliters. In this case, 0.475 L multiplied by 1,000 mL/L gives you 475 mL. This conversion is essential in laboratory procedures where precise measurements are crucial for experiments.

To convert microliters to liters, use the conversion factor that 1 µL equals 10⁻⁶ L. Therefore, to convert 3,250 µL to liters, multiply 3,250 by 10⁻⁶. This calculation yields 3,250 x 10⁻⁶ = 0.00325 L. Thus, 3,250 microliters is equivalent to 0.00325 liters.

To convert the mass from kilograms to milligrams, first convert kilograms to grams using the conversion factor (1 kg = 1,000 g). Therefore, 5.92 × 10⁻⁵ kg equals 5.92 × 10⁻² g, or 0.0592 g. Next, convert grams to milligrams (1 g = 1,000 mg), resulting in 0.0592 g × 1,000 mg/g = 59.2 mg. This shows that the mass of 5.92 × 10⁻⁵ kg is equivalent to 59.2 mg.

To find the density of the liquid, divide its mass by its volume. First, convert the mass from kilograms to grams: 0.0836 kg equals 83.6 g. Since the volume is given in milliliters, it can be directly used as 62.4 cm³. The formula for density is density = mass/volume. Thus, density = 83.6 g / 62.4 cm³, which equals approximately 1.34 g/cm³ when rounded to two decimal places. This value indicates the mass of the liquid per unit volume, providing insight into its properties.

To convert milliliters to liters, divide the volume in milliliters by 1,000, since 1 liter equals 1,000 milliliters. For 850 mL, the calculation is 850 ÷ 1,000, which equals 0.850 L. This shows that 850 mL is equivalent to 0.850 liters, making it the correct conversion.

To convert from kilograms to milligrams, multiply the mass in kilograms by 1,000,000 (since 1 kg = 1,000,000 mg). For a mass of 7.15 × 10⁻⁴ kg, the calculation is:

7.15 × 10⁻⁴ kg × 1,000,000 mg/kg = 715 mg.

This shows that the mass in milligrams is 715, which is the correct conversion from the original measurement in kilograms.

To convert grams to milligrams, it's essential to understand the metric system's prefixes. The prefix "milli-" denotes a factor of one-thousandth (1/1000). Therefore, 1 gram, which is equal to 1,000 milligrams, reflects this relationship. This conversion is crucial in various fields, such as medicine and chemistry, where precise measurements are necessary. Thus, for every gram, there are 1,000 milligrams.

To find the density of the liquid, use the formula: density = mass/volume. The mass is given as 0.1248 kg, which is equivalent to 124.8 g (since 1 kg = 1000 g). The volume of the liquid is 78.0 mL, which is the same as 78.0 cm³ (since 1 mL = 1 cm³). Therefore, the density calculation is 124.8 g / 78.0 cm³ = 1.60 g/cm³. Rounding to two decimal places confirms the final density value.

To convert microliters (µL) to liters (L), you multiply the volume in µL by the conversion factor, which is 10⁻⁶ L/µL. For 1,750 µL, the calculation is: 1,750 µL × 10⁻⁶ L/µL = 1,750 × 0.000001 L = 0.00175 L. This shows that the volume in liters is 0.00175 L.

To find the mass of the forensic sample, use the formula: mass = density × volume. Here, the density is 2.35 g/cm³ and the volume is 15.0 cm³. Multiplying these gives: 2.35 g/cm³ × 15.0 cm³ = 35.25 g. To convert grams to kilograms, divide by 1000, resulting in 35.25 g ÷ 1000 = 0.03525 kg. Thus, the mass of the sample is 0.03525 kg.