Calculate { (5.4) \cdot (2.4)$}$.
Introduction to Multiplication of Decimal Numbers
Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number. When dealing with decimal numbers, it's essential to understand the rules and procedures for multiplying them. In this article, we will focus on calculating the product of two decimal numbers, {(5.4) \cdot (2.4)$}$, and explore the steps involved in performing this operation.
Understanding Decimal Numbers
Decimal numbers are a type of real number that can be expressed in the form {a.b$}$, where {a$}$ is the whole number part and {b$}$ is the fractional part. In the given problem, we have two decimal numbers: ${5.4\$} and ${2.4\$}. To calculate their product, we need to follow the rules of multiplication.
Rules for Multiplying Decimal Numbers
When multiplying decimal numbers, we need to follow the rules below:
- Multiply the whole number parts together.
- Multiply the fractional parts together.
- Multiply the whole number part by the fractional part.
- Multiply the fractional part by the whole number part.
- Add the products obtained in steps 3 and 4.
Step-by-Step Calculation
To calculate the product of {(5.4) \cdot (2.4)$}$, we will follow the steps outlined above.
Step 1: Multiply the Whole Number Parts Together
The whole number part of ${5.4\$} is ${5\$}, and the whole number part of ${2.4\$} is ${2\$}. We multiply these two numbers together:
${5 \cdot 2 = 10\$}
Step 2: Multiply the Fractional Parts Together
The fractional part of ${5.4\$} is ${0.4\$}, and the fractional part of ${2.4\$} is ${0.4\$}. We multiply these two numbers together:
${0.4 \cdot 0.4 = 0.16\$}
Step 3: Multiply the Whole Number Part by the Fractional Part
We multiply the whole number part of ${5.4\$} by the fractional part of ${2.4\$}:
${5 \cdot 0.4 = 2\$}
Step 4: Multiply the Fractional Part by the Whole Number Part
We multiply the fractional part of ${5.4\$} by the whole number part of ${2.4\$}:
${0.4 \cdot 2 = 0.8\$}
Step 5: Add the Products Obtained in Steps 3 and 4
We add the products obtained in steps 3 and 4:
${2 + 0.8 = 2.8\$}
Step 6: Multiply the Products Obtained in Steps 1 and 2
We multiply the products obtained in steps 1 and 2:
${10 \cdot 0.16 = 1.6\$}
Step 7: Add the Products Obtained in Steps 5 and 6
We add the products obtained in steps 5 and 6:
${2.8 + 1.6 = 4.4\$}
Conclusion
In this article, we calculated the product of two decimal numbers, {(5.4) \cdot (2.4)$}$, by following the rules of multiplication. We multiplied the whole number parts together, multiplied the fractional parts together, multiplied the whole number part by the fractional part, multiplied the fractional part by the whole number part, and added the products obtained in steps 3 and 4. The final result is ${4.4\$}.
Frequently Asked Questions
- What is the product of {(5.4) \cdot (2.4)$}$?
- The product of {(5.4) \cdot (2.4)$}$ is ${4.4\$}.
- How do I multiply decimal numbers?
- To multiply decimal numbers, you need to follow the rules outlined above.
- What are the rules for multiplying decimal numbers?
- The rules for multiplying decimal numbers are:
- Multiply the whole number parts together.
- Multiply the fractional parts together.
- Multiply the whole number part by the fractional part.
- Multiply the fractional part by the whole number part.
- Add the products obtained in steps 3 and 4.
- The rules for multiplying decimal numbers are:
References
Introduction
Multiplication of decimal numbers is a fundamental operation in mathematics that involves the repeated addition of a number. In this article, we will address some of the most frequently asked questions about multiplication of decimal numbers, including the rules for multiplying decimal numbers, how to multiply decimal numbers, and examples of multiplication of decimal numbers.
Q&A
Q: What are the rules for multiplying decimal numbers?
A: The rules for multiplying decimal numbers are:
- Multiply the whole number parts together.
- Multiply the fractional parts together.
- Multiply the whole number part by the fractional part.
- Multiply the fractional part by the whole number part.
- Add the products obtained in steps 3 and 4.
Q: How do I multiply decimal numbers?
A: To multiply decimal numbers, you need to follow the rules outlined above. Here's an example:
Suppose we want to multiply ${5.4\$} and ${2.4\$}. We would follow these steps:
- Multiply the whole number parts together: ${5 \cdot 2 = 10\$}
- Multiply the fractional parts together: ${0.4 \cdot 0.4 = 0.16\$}
- Multiply the whole number part by the fractional part: ${5 \cdot 0.4 = 2\$}
- Multiply the fractional part by the whole number part: ${0.4 \cdot 2 = 0.8\$}
- Add the products obtained in steps 3 and 4: ${2 + 0.8 = 2.8\$}
- Multiply the products obtained in steps 1 and 2: ${10 \cdot 0.16 = 1.6\$}
- Add the products obtained in steps 5 and 6: ${2.8 + 1.6 = 4.4\$}
Q: What is the product of {(5.4) \cdot (2.4)$}$?
A: The product of {(5.4) \cdot (2.4)$}$ is ${4.4\$}.
Q: How do I multiply decimals with different numbers of decimal places?
A: To multiply decimals with different numbers of decimal places, you need to follow the rules outlined above. Here's an example:
Suppose we want to multiply ${5.4\$} and ${2.00\$}. We would follow these steps:
- Multiply the whole number parts together: ${5 \cdot 2 = 10\$}
- Multiply the fractional parts together: ${0.4 \cdot 0.00 = 0\$}
- Multiply the whole number part by the fractional part: ${5 \cdot 0.00 = 0\$}
- Multiply the fractional part by the whole number part: ${0.4 \cdot 2 = 0.8\$}
- Add the products obtained in steps 3 and 4: ${0 + 0.8 = 0.8\$}
- Multiply the products obtained in steps 1 and 2: ${10 \cdot 0 = 0\$}
- Add the products obtained in steps 5 and 6: ${0.8 + 0 = 0.8\$}
Q: What are some examples of multiplication of decimal numbers?
A: Here are some examples of multiplication of decimal numbers:
- {(5.4) \cdot (2.4) = 4.4$}$
- {(5.4) \cdot (2.00) = 10.8$}$
- {(5.4) \cdot (0.4) = 2.16$}$
- {(2.4) \cdot (5.4) = 12.96$}$
Conclusion
In this article, we addressed some of the most frequently asked questions about multiplication of decimal numbers, including the rules for multiplying decimal numbers, how to multiply decimal numbers, and examples of multiplication of decimal numbers. We hope that this article has provided you with a better understanding of multiplication of decimal numbers and how to apply this operation in real-world situations.
Frequently Asked Questions
- What are the rules for multiplying decimal numbers?
- The rules for multiplying decimal numbers are:
- Multiply the whole number parts together.
- Multiply the fractional parts together.
- Multiply the whole number part by the fractional part.
- Multiply the fractional part by the whole number part.
- Add the products obtained in steps 3 and 4.
- The rules for multiplying decimal numbers are:
- How do I multiply decimal numbers?
- To multiply decimal numbers, you need to follow the rules outlined above.
- What is the product of {(5.4) \cdot (2.4)$}$?
- The product of {(5.4) \cdot (2.4)$}$ is ${4.4\$}.
- How do I multiply decimals with different numbers of decimal places?
- To multiply decimals with different numbers of decimal places, you need to follow the rules outlined above.
- What are some examples of multiplication of decimal numbers?
- Here are some examples of multiplication of decimal numbers:
- {(5.4) \cdot (2.4) = 4.4$}$
- {(5.4) \cdot (2.00) = 10.8$}$
- {(5.4) \cdot (0.4) = 2.16$}$
- {(2.4) \cdot (5.4) = 12.96$}$
- Here are some examples of multiplication of decimal numbers: