Question

Perform the following conversions. a) \(3.4 \times 10^{2} \mathrm{~cm} / \mathrm{s}\) to centimeters/minute b) \(26.6 \mathrm{~mm} / \mathrm{s}\) to millimeters/hour c) \(13.7 \mathrm{~kg} / \mathrm{L}\) to kilograms/milliliters

Short answer

a) 20400 cm/minute, b) 95760 mm/hour, c) 0.0137 kg/mL

Step-by-step solution

Convert Centimeters per Second to Centimeters per Minute

To convert from centimeters per second to centimeters per minute, you need to multiply by the number of seconds in a minute. There are 60 seconds in a minute. Therefore, you multiply the given rate by 60: \[ 3.4 \times 10^2 \frac{\text{cm}}{\text{s}} \times 60 \frac{\text{s}}{\text{minute}} = 20400 \frac{\text{cm}}{\text{minute}} \]

Convert Millimeters per Second to Millimeters per Hour

To convert from millimeters per second to millimeters per hour, multiply by the number of seconds in an hour. There are 3600 seconds in an hour (60 minutes/hour * 60 seconds/minute). Thus, you multiply:\[ 26.6 \frac{\text{mm}}{\text{s}} \times 3600 \frac{\text{s}}{\text{hour}} = 95760 \frac{\text{mm}}{\text{hour}} \]

Convert Kilograms per Liter to Kilograms per Milliliter

When converting from kilograms per liter to kilograms per milliliter, consider the relationship between liters and milliliters: 1 liter = 1000 milliliters. Therefore, divide by 1000:\[ 13.7 \frac{\text{kg}}{\text{L}} \times \frac{1}{1000 \frac{\text{L}}{\text{mL}}} = 0.0137 \frac{\text{kg}}{\text{mL}} \]

Key concepts

Understanding Centimeters per Minute

The concept of "Centimeters per Minute" is a unit of speed that shows how many centimeters an object travels in one minute. To convert a given speed from centimeters per second to centimeters per minute, you need to consider how many seconds are in one minute. It's essential to know the basic time conversion: 60 seconds make up 1 minute. Therefore, when you have a speed in centimeters per second, you'll multiply by 60 to switch to centimeters per minute.For example, if you start with the speed of \(3.4 \times 10^2\) cm/s, your calculation would look like this:

• Take the original speed: \(3.4 \times 10^2\) cm/s.
• Multiply by 60 because there are 60 seconds in a minute.
• The result is: \(3.4 \times 10^2 \times 60 = 20400\) cm/min.

So, 340 cm/s is converted to 20,400 cm/min. This unit conversion is useful when you need to think about speeds over longer periods, like transport speeds or growth rates.

Exploring Millimeters per Hour

"Millimeters per Hour" is another way to measure speed, showing how many millimeters something moves in an hour. When you're converting from millimeters per second to millimeters per hour, it's crucial to know the number of seconds in one hour.There are 3600 seconds in an hour because 1 hour has 60 minutes, and each minute has 60 seconds. Thus, you multiply the speed by 3600 to perform the conversion.For instance, starting with a rate of 26.6 mm/s, you can calculate:

• Use the original rate: 26.6 mm/s.
• Multiply by 3600 because there are 3600 seconds in an hour.
• Gives you: \(26.6 \times 3600 = 95760\) mm/hr.

This shows that at a rate of 26.6 mm/s, something would move 95,760 millimeters in one hour, useful for assessing longer-distance travel or processing speeds.

Decoding Kilograms per Milliliter

"Kilograms per Milliliter" is a density measurement, indicating how much mass (in kilograms) is present per unit volume (in milliliters). When converting from kilograms per liter to kilograms per milliliter, understanding the relationship between liters and milliliters is key.A liter is a larger unit than a milliliter. Specifically, there are 1000 milliliters in a liter. So, to convert a value from kg/L to kg/mL, you divide by 1000.Let's take a practical example with the density of 13.7 kg/L:

• Start with the density: 13.7 kg/L.
• Divide by 1000, since 1 liter = 1000 milliliters.
• The calculation is: \(13.7 \div 1000 = 0.0137\) kg/mL.

This conversion helps in applications where small volumes are considered, like pharmaceutical formulations or food sciences, where density impacts the formulation.