Question

Write the conversion factors for each of the following statements: a. A bee flies at an average speed of \(3.5 \mathrm{~m}\) per second. b. The daily value for potassium is \(3500 \mathrm{mg}\). c. An automobile traveled \(46.0 \mathrm{~km}\) on \(1.0\) gal of gasoline. d. The label on a bottle reads \(50 \mathrm{mg}\) of Atenolol per tablet. e. The pesticide level in plums was 29 ppb. f. A low-dose aspirin contains \(81 \mathrm{mg}\) of aspirin per tablet.

Short answer

a. \(3.5 \text{ m/s}\); b. \(3500 \text{ mg}\); c. \(46.0 \text{ km/gal}\); d. \(50 \text{ mg/tablet}\); e. \(29 \text{ ppb}\); f. \(81 \text{ mg/tablet}\).

Step-by-step solution

Identifying Units and Values

For each statement, identify the units involved and the numerical values. Write down these units and values to use them in the conversion factors.

Converting Speed of Bee

Start with the bee's speed: \(3.5 \text{ m/s}\). The conversion factor for speed will be \(1\text{ s} / 3.5 \text{ m}\) or \(3.5 \text{ m} / 1\text{ s}\).

Converting Daily Value for Potassium

For potassium, the daily value is given as \(3500 \text{ mg}\). This can be written as \(1 \text{ daily value} / 3500 \text{ mg}\) or \(3500 \text{ mg} / 1 \text{ daily value}\).

Converting Automobile's Fuel Efficiency

The automobile traveled \(46.0 \text{ km}\) on \(1.0 \text{ gal}\) of gasoline. The conversion factor here is \(1.0 \text{ gal} / 46.0 \text{ km}\) or \(46.0 \text{ km} / 1.0 \text{ gal}\).

Converting Atenolol Dosage

The label on a bottle reads \(50 \text{ mg/tablet}\). Write the conversion factor as \(50 \text{ mg} / 1 \text{ tablet}\) or \(1 \text{ tablet} / 50 \text{ mg}\).

Converting Pesticide Level

The pesticide level in plums is measured as \(29 \text{ ppb}\). The conversion factor for this is \(29 \text{ ppb} / 1\text{ level}\) or \(1\text{ level} / 29 \text{ ppb}\).

Converting Aspirin Dosage

A low-dose aspirin contains \(81 \text{ mg/tablet}\). This can be represented as \(81 \text{ mg} / 1 \text{ tablet}\) or \(1 \text{ tablet} / 81 \text{ mg}\).

Key concepts

Unit Conversion

Unit conversion refers to the process of converting a measurement from one unit to another. This is particularly important when dealing with different measurement systems, such as converting miles to kilometers or grams to milligrams. For example, if you have a bee flying at 3.5 meters per second (m/s), you might need to convert this to kilometers per hour (km/h) for better context. Understanding conversion factors, such as 1 meter is equal to 0.001 kilometers or 1 second is equal to 1/3600 hours, aids in making these changes.

Speed Calculation

Speed calculation is essential in physics and everyday scenarios, like knowing how fast a bee flies or how quickly an automobile travels. Speed is typically represented as distance traveled per unit of time. For instance, the speed of a bee is given as 3.5 meters per second (m/s). To convert this speed:

• Multiply 3.5 m by 3600 (the number of seconds in an hour) to get meters per hour.
• Divide by 1000 (to convert meters to kilometers).

This helps in expressing speed in different units, such as kilometers per hour (km/h).

Dosage Conversion

Dosage conversion is crucial in healthcare to ensure proper medication administration. Dosages are often listed in milligrams per tablet (mg/tablet), which need to be converted based on patient needs or other measurements. For example, if a tablet contains 50 mg of Atenolol:

• The conversion factor is 50 mg per tablet.
• This can also be expressed as 1 tablet per 50 mg.

This understanding is vital for accurate medication dosages and patient safety.

Fuel Efficiency

Fuel efficiency measures how far an automobile can travel per unit of fuel. For example, an automobile traveled 46.0 kilometers on 1.0 gallon of gasoline. To convert fuel efficiency:

• Use the conversion factor 1 gallon per 46.0 kilometers.
• Alternatively, 46.0 kilometers per 1 gallon.

Converting these units helps in comparing different vehicles' fuel efficiency, improving cost-effectiveness, and supporting environmental sustainability.

Pesticide Levels

Pesticide levels in food and the environment are often measured in parts per billion (ppb). For example, the pesticide level in plums is 29 ppb. Conversion involves understanding and comparing these values for safety standards. For instance, a conversion factor of 29 ppb per level, or 1 level per 29 ppb, helps to standardize and interpret pesticide content against regulated limits.

Daily Nutritional Values

Daily nutritional values indicate the required intake of nutrients essential for health. For example, the daily value for potassium is 3500 milligrams (mg). To express this in conversions:

• Use 3500 mg per daily value.
• Alternatively, 1 daily value per 3500 mg.

Such conversions are critical for dietary planning and ensuring that nutritional intakes meet the recommended guidelines for maintaining good health.