Question

Add the following decimals. If you administer two tablets labeled \(0.04 \mathrm{mg},\) what total dosage will you administer?

Short answer

The total dosage is 0.08 mg.

Step-by-step solution

Identify the Decimal Numbers

We are given two tablets each labeled with a dosage of \(0.04\, \mathrm{mg}\). This means we need to add \(0.04\, \mathrm{mg}\) and \(0.04\, \mathrm{mg}\) to find the total dosage.

Perform the Addition

Add the two decimal numbers: \(0.04 + 0.04\). Start from the rightmost digit, which is the hundredths place.\[0.04 \+ 0.04 \= 0.08\]

Evaluate the Result

The result of the addition is \(0.08\). Therefore, the total dosage administered when two tablets are taken is \(0.08 \, \mathrm{mg}\).

Key concepts

Dosage Calculation

Dosage calculation ensures that the correct amount of medication is administered, which is crucial for patient safety. When calculating the dosage of a medication, especially in the case of tablets or capsules, it involves understanding the label on the medication. Here, we have tablets labeled at \(0.04\, \mathrm{mg}\). To find out the total dosage, we need to add the dosage of each tablet together. For example, if you are giving two tablets, each containing \(0.04\, \mathrm{mg}\), you would need to calculate:

• Determining the number of tablets: 2 tablets
• The dose per tablet: \(0.04\, \mathrm{mg}\)
• Multiply dose per tablet by number of tablets: \(0.04 \times 2 = 0.08\, \mathrm{mg}\)

This arithmetic brings us to our next topic, which is decimal mathematics. Understanding the math behind dosage calculation helps ensure we're administering the correct amount safely.

Decimal Mathematics

Decimal mathematics deals with numbers expressed in decimal form, where digits are placed to the right of the decimal point to signify values less than one whole number. In our exercise example, each tablet has a dosage of \(0.04\, \mathrm{mg}\), a straightforward decimal number. Adding decimal numbers follows similar rules as whole numbers, with attention to the decimal point and place values:

• Align the numbers by their decimal points.
• Fill in any missing digits with zeros for balance.
• Add the numbers starting from the rightmost decimal place (the hundredths place here).

For clarity, the addition in our example problem follows:\[0.04 + 0.04 = 0.08\]Understanding how the place values work is key in attaining the correct result. The ten-hundredth plus ten-hundredth makes two hundredths, giving a total of \(0.08\). Decimal addition like this is essential in fields like pharmacy and medicine, where precise measurements can have significant impacts.

Basic Arithmetic Steps

Basic arithmetic is the foundation of more complex calculations, and mastery of these steps can greatly aid in problems like the dosage calculation. The basic arithmetic operations are addition, subtraction, multiplication, and division, and each has rules that must be followed for proper execution.In the context of our exercise, we focus on addition, particularly of decimals. Here’s how you can simplify the addition of decimal numbers:

• Identify and write down the decimal numbers to be added.
• Ensure the decimal points are aligned to prevent errors.
• Begin adding from the rightmost decimal digit, carrying over to the next left digit if necessary.
• For results ending in zeros right of the decimal, those can be omitted in the final answer format, e.g., \(0.080\) can be simplified to \(0.08\).

These steps help in achieving precision, reinforcing skills crucial for accurately handling problems in both academic and real-world scenarios.