Question

Add the following decimals. You have just administered 3 tablets with dose strength of \(1.5 \mathrm{mg}\) each. What was the total dosage?

Short answer

The total dosage is 4.5 mg.

Step-by-step solution

Understand the Problem

We need to find the total dosage given that each tablet contains a dose of \(1.5\) mg, and \(3\) tablets have been administered.

Set Up the Addition

To find the total dosage, we multiply the dosage of one tablet by the number of tablets. We express this as a multiplication problem: \(1.5 \times 3\).

Perform the Multiplication

Calculate the multiplication \(1.5 \times 3\). This can be thought of as adding \(1.5\) three times: \(1.5 + 1.5 + 1.5 = 4.5\).

Verify the Calculation

Ensure the multiplication is correct: \(1.5 \times 3 = 4.5\). We've correctly added \(3\) doses of \(1.5\) mg to obtain \(4.5\) mg.

Key concepts

Decimal Multiplication

Decimal multiplication is an important concept, particularly when dealing with real-world situations like dosage calculation. When we multiply decimals, the approach is similar to multiplying whole numbers. The key is to keep track of the decimal place.

In the exercise, we multiplied the dose of a single tablet, which is 1.5 mg, by the number of tablets, which is 3. To do this multiplication:

• Consider the problem as multiplying two whole numbers: 15 and 3.
• After multiplying, you get 45. But you must remember that the decimal was moved one place to the left in the original number "1.5." So, the result is 4.5.

This method ensures that the decimal point is accurately placed in your final answer, leading to the correct dosage calculation of 4.5 mg.

Medication Dosing

Medication dosing requires careful calculations to ensure safety and effectiveness. Understanding how to calculate doses, particularly with decimal numbers, is critical in healthcare. When dealing with medication dosing, pay attention to:

• The strength of each dose.
• The number of doses prescribed.
• Multiplying these factors to find the total dose.

For example, when administering 3 tablets each containing 1.5 mg, we multiply 1.5 by 3, which results in a total of 4.5 mg. It's crucial to check calculations to prevent errors that could lead to overdosing or underdosing.

Mathematics in Healthcare

Mathematics plays a pivotal role in healthcare, aiding in precise calculations that impact patient safety. Calculations such as dosage, conversions, and ratios are daily tasks for healthcare professionals.

In the context of medication dosing, mathematics ensures:

• Accurate dosage based on the prescription.
• Proper conversion from one measurement unit to another if needed.
• Calculating the total dosage over different periods or combinations of medications.

Using mathematics, professionals can avoid dangerous errors, making it essential for quality care. Precision in these calculations is non-negotiable, reflecting the importance of robust mathematical skills in healthcare settings.