Question

Identify the numbers in each of the following statements as measured or exact: a. A patient weighs \(155 \mathrm{lb}\). b. A patient is given 2 tablets of medication. c. In the metric system, \(1 \mathrm{~kg}\) is equal to \(1000 \mathrm{~g}\). d. The distance from Denver, Colorado, to Houston, Texas, is \(1720 \mathrm{~km}\).

Short answer

Measured: 155 lb, 1720 km. Exact: 2 tablets, 1 kg = 1000 g.

Step-by-step solution

Identify the Patient's Weight (Part a)

The weight of the patient is given as 155 lb. This kind of measurement can vary slightly, so it is considered a measured number because it's obtained through a measurement process.

Identify the Number of Tablets (Part b)

The patient is given 2 tablets. This is an exact number because you can count the number of tablets directly without any measurement.

Metric System Conversion (Part c)

In the metric system, 1 kg is equal to 1000 g. This is an exact number because it is a defined conversion factor within the metric system.

Identify the Distance Between Cities (Part d)

The distance from Denver, Colorado, to Houston, Texas, is 1720 km. This measurement can vary and is considered measured because it depends on how the distance is determined.

Key concepts

measured numbers

In chemistry and many other scientific fields, measured numbers come from measurements. These numbers possess some degree of uncertainty because they depend on the precision of the instrument used to make the measurement.
Examples of measured numbers include weights, lengths, volumes, and temperatures.
For instance, in our original exercise, the weight of a patient is given as 155 lb. This is a measured number because it can vary slightly depending on the accuracy of the scale used.
When dealing with measured numbers, it is essential to report the number of significant figures correctly. This practice helps to convey the precision of the measurement.

exact numbers

Exact numbers, unlike measured numbers, have no uncertainty. They are defined values or countable quantities.
Examples include the number of objects and defined conversion factors.
In the exercise, the number of tablets given to a patient is 2. This is an exact number because it is counted directly. Likewise, in the metric system, the conversion factor where 1 kg equals 1000 g is an exact number. This is because it is a defined relationship within the system.
Exact numbers are important when performing calculations, as they do not introduce any error into the results.

metric system conversions

Metric system conversions involve changing measurements from one unit to another within the metric system. This system is based on powers of ten, making conversions straightforward and exact.
For example, as highlighted in the exercise, 1 kg is exactly equal to 1000 g. This conversion is precise because it comes from the defined standards of the metric system.
Common metric system conversions include:

• 1 meter (m) = 100 centimeters (cm)
• 1 liter (L) = 1000 milliliters (mL)
• 1 kilogram (kg) = 1000 grams (g)

Understanding and using these precise conversions is crucial in scientific tasks involving measurements.

unit measurement

Unit measurement involves the determination of the quantity of something using established standard units.
Different units are used for different types of measurements, including:

• Mass (grams, kilograms)
• Length (meters, centimeters)
• Volume (liters, milliliters)

In the exercise, the distance from Denver to Houston is given as 1720 km. This is an example of a unit measurement, though it is a measured number because the exact distance can vary slightly.
When performing calculations, it is vital to use consistent units to ensure accuracy in the results. Unit conversions, especially within the metric system, enable precise and straightforward calculations.