Carry out the following conversions: (c) 8.75 mm/s to km/hr (f) 8.75 lb/ft³ to g/mL.

Verified step by step guidance

To convert 8.75 mm/s to km/hr, start by converting millimeters to kilometers. There are 1,000,000 millimeters in a kilometer, so divide the value in millimeters by 1,000,000.

Next, convert seconds to hours. There are 3600 seconds in an hour, so multiply the value in seconds by 3600.

Combine these conversions: \( \text{km/hr} = \left( \frac{8.75 \text{ mm/s}}{1,000,000} \right) \times 3600 \).

For the conversion of 8.75 lb/ft³ to g/mL, start by converting pounds to grams. There are 453.592 grams in a pound, so multiply the value in pounds by 453.592.

Next, convert cubic feet to milliliters. There are 28,316.8 milliliters in a cubic foot, so divide the value in cubic feet by 28,316.8. Combine these conversions: \( \text{g/mL} = \left( 8.75 \text{ lb/ft}^3 \times 453.592 \right) / 28,316.8 \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. This involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. For example, to convert from millimeters per second to kilometers per hour, one must know the relationships between these units, such as 1 km = 1,000 m and 1 hour = 3,600 seconds.

Density and Mass-Volume Relationships

Density is defined as mass per unit volume and is typically expressed in units such as grams per milliliter (g/mL) or pounds per cubic foot (lb/ft³). Understanding density is crucial for converting between mass and volume measurements, as it allows for the calculation of how much mass is contained in a given volume of a substance. For instance, knowing the density of a material can help convert its weight in lb/ft³ to its equivalent in g/mL.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert units by treating the units as algebraic quantities. This method involves multiplying the original measurement by conversion factors that cancel out the unwanted units, leaving the desired units. It is a systematic approach that ensures accuracy in conversions and helps verify that the final answer is dimensionally consistent.