Calculate The Following:$\[ 1.3 \times 3.6 = \\]A. 4.9 B. 4.68 C. 4.58 D. 46.8
Introduction
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 accurately. In this article, we will explore the concept of multiplying decimal numbers, provide a step-by-step guide, and apply it to a specific problem.
Understanding Decimal Numbers
Decimal numbers are numbers that have a decimal point, which separates the whole number part from the fractional part. For example, 3.6 is a decimal number that consists of a whole number part (3) and a fractional part (0.6). When multiplying decimal numbers, it's crucial to understand the concept of place value and how it affects the multiplication process.
Multiplication of Decimal Numbers: A Step-by-Step Guide
To multiply decimal numbers, follow these steps:
- Line up the decimal points: When multiplying decimal numbers, it's essential to line up the decimal points. This will help you determine the correct placement of the decimal point in the final answer.
- Multiply the numbers: Multiply the numbers as if they were whole numbers. For example, if you're multiplying 3.6 by 1.3, multiply 36 by 13.
- Count the total number of decimal places: Count the total number of decimal places in the two numbers being multiplied. In the example above, 3.6 has 1 decimal place, and 1.3 has 1 decimal place, so the total number of decimal places is 2.
- Place the decimal point: Place the decimal point in the final answer based on the total number of decimal places counted in step 3.
Applying the Rules to a Specific Problem
Now that we've covered the rules for multiplying decimal numbers, let's apply them to the problem:
Calculate the following: $1.3 \times 3.6 = $
To solve this problem, follow the steps outlined above:
- Line up the decimal points: Line up the decimal points in the two numbers being multiplied.
- Multiply the numbers: Multiply 36 by 13.
- Count the total number of decimal places: Count the total number of decimal places in the two numbers being multiplied. In this case, both numbers have 1 decimal place, so the total number of decimal places is 2.
- Place the decimal point: Place the decimal point in the final answer based on the total number of decimal places counted in step 3.
Solution
To solve the problem, multiply 36 by 13:
36 × 13 = 468
Since both numbers have 1 decimal place, the total number of decimal places is 2. Therefore, place the decimal point 2 places from the right in the final answer:
4.68
Conclusion
Multiplication of decimal numbers is a fundamental operation in mathematics that requires a clear understanding of the rules and procedures. By following the steps outlined above, you can accurately multiply decimal numbers and apply the rules to specific problems. In this article, we applied the rules to the problem $1.3 \times 3.6 = $ and arrived at the solution 4.68.
Frequently Asked Questions
Q: What is the rule for multiplying decimal numbers?
A: The rule for multiplying decimal numbers is to line up the decimal points, multiply the numbers as if they were whole numbers, count the total number of decimal places, and place the decimal point in the final answer based on the total number of decimal places.
Q: How do I determine the correct placement of the decimal point in the final answer?
A: To determine the correct placement of the decimal point in the final answer, count the total number of decimal places in the two numbers being multiplied and place the decimal point in the final answer based on that count.
Q: What is the solution to the problem $1.3 \times 3.6 = $?
A: The solution to the problem $1.3 \times 3.6 = $ is 4.68.
Q: Why is it essential to understand the concept of place value when multiplying decimal numbers?
Introduction
Multiplication of decimal numbers is a fundamental operation in mathematics that requires a clear understanding of the rules and procedures. In this article, we will address some of the most frequently asked questions related to multiplication of decimal numbers.
Q&A
Q: What is the rule for multiplying decimal numbers?
A: The rule for multiplying decimal numbers is to line up the decimal points, multiply the numbers as if they were whole numbers, count the total number of decimal places, and place the decimal point in the final answer based on the total number of decimal places.
Q: How do I determine the correct placement of the decimal point in the final answer?
A: To determine the correct placement of the decimal point in the final answer, count the total number of decimal places in the two numbers being multiplied and place the decimal point in the final answer based on that count.
Q: What is the difference between multiplying decimal numbers and multiplying whole numbers?
A: The main difference between multiplying decimal numbers and multiplying whole numbers is the placement of the decimal point in the final answer. When multiplying decimal numbers, you need to count the total number of decimal places and place the decimal point accordingly.
Q: Can I multiply decimal numbers without lining up the decimal points?
A: No, it's essential to line up the decimal points when multiplying decimal numbers. This ensures that the decimal point is placed correctly in the final answer.
Q: How do I handle zeros when multiplying decimal numbers?
A: When multiplying decimal numbers, zeros are treated as placeholders. If a number has a zero in the decimal place, it's essential to include that zero in the multiplication process.
Q: Can I multiply decimal numbers with different numbers of decimal places?
A: Yes, you can multiply decimal numbers with different numbers of decimal places. However, you need to count the total number of decimal places and place the decimal point accordingly in the final answer.
Q: What is the solution to the problem $1.3 \times 3.6 = $?
A: The solution to the problem $1.3 \times 3.6 = $ is 4.68.
Q: Why is it essential to understand the concept of place value when multiplying decimal numbers?
A: It's essential to understand the concept of place value when multiplying decimal numbers because it affects the multiplication process and the placement of the decimal point in the final answer.
Q: Can I use a calculator to multiply decimal numbers?
A: Yes, you can use a calculator to multiply decimal numbers. However, it's essential to understand the rules and procedures for multiplying decimal numbers to ensure accuracy.
Q: How do I check my answer when multiplying decimal numbers?
A: To check your answer when multiplying decimal numbers, multiply the numbers again and compare the result with your original answer. If the results match, your answer is correct.
Conclusion
Multiplication of decimal numbers is a fundamental operation in mathematics that requires a clear understanding of the rules and procedures. By addressing some of the most frequently asked questions related to multiplication of decimal numbers, we hope to provide a better understanding of this concept and help you become more confident in your math skills.
Additional Resources
- Math is Fun: Multiplication of Decimal Numbers
- Khan Academy: Multiplication of Decimal Numbers
- Math Open Reference: Multiplication of Decimal Numbers
Practice Problems
- $2.5 \times 3.8 = $
- $4.2 \times 2.1 = $
- $1.9 \times 3.5 = $