Multiply.$4.83 \times 7.1$Enter Your Answer In The Box.$\square$

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Understanding the Problem

When faced with a multiplication problem involving decimals, it's essential to understand the concept of multiplying numbers with decimal places. In this case, we're required to multiply $4.83$ by $7.1$. To approach this problem, we need to follow the standard procedure for multiplying decimals, which involves multiplying the numbers as if they were whole numbers and then placing the decimal point in the correct position.

Multiplying Decimals

To multiply decimals, we can use the following steps:

1. Multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in the factors.
3. Place the decimal point in the product at the correct position, which is determined by the total number of decimal places in the factors.

Applying the Steps to the Problem

Let's apply the steps to the problem of multiplying $4.83$ by $7.1$.

Step 1: Multiply the Numbers as if They Were Whole Numbers

First, we multiply $4.83$ by $7.1$ as if they were whole numbers.

$4.83 \times 7.1 = 34.293$

Step 2: Count the Total Number of Decimal Places in the Factors

Next, we count the total number of decimal places in the factors. $4.83$ has $2$ decimal places, and $7.1$ has $1$ decimal place. Therefore, the total number of decimal places is $2 + 1 = 3$.

Step 3: Place the Decimal Point in the Product

Finally, we place the decimal point in the product at the correct position, which is determined by the total number of decimal places in the factors. Since the total number of decimal places is $3$, we place the decimal point $3$ places from the right in the product.

$34.293 \rightarrow 34.293$

Calculating the Final Answer

Now that we have followed the steps, we can calculate the final answer.

$4.83 \times 7.1 = 34.293$

Conclusion

In conclusion, multiplying decimals involves multiplying the numbers as if they were whole numbers and then placing the decimal point in the correct position. By following the steps outlined above, we can accurately multiply decimals and obtain the correct answer.

Example Use Cases

Multiplying decimals is a fundamental operation in mathematics, and it has numerous applications in real-world scenarios. Here are a few example use cases:

• Finance: When calculating interest rates or investment returns, we often need to multiply decimals. For instance, if an investment earns a $4.83\%$ annual return and we invest $7.1$ times the initial amount, we need to multiply $4.83\%$ by $7.1$ to determine the total return.
• Science: In scientific calculations, we often need to multiply decimals to obtain accurate results. For example, if we're calculating the volume of a rectangular prism with dimensions $4.83$ cm by $7.1$ cm by $2$ cm, we need to multiply the dimensions to obtain the volume.
• Engineering: In engineering applications, we often need to multiply decimals to design and optimize systems. For instance, if we're designing a mechanical system with a $4.83$ mm diameter pipe and a $7.1$ mm diameter pipe, we need to multiply the diameters to determine the total cross-sectional area.

Tips and Tricks

Here are a few tips and tricks to help you multiply decimals accurately:

• Use a calculator: When multiplying decimals, it's often easier to use a calculator to avoid errors.
• Line up the decimal points: When multiplying decimals, make sure to line up the decimal points in the factors to ensure accurate placement of the decimal point in the product.
• Check your work: Always check your work by multiplying the factors as if they were whole numbers and then placing the decimal point in the correct position.

Common Mistakes to Avoid

Here are a few common mistakes to avoid when multiplying decimals:

• Incorrect placement of the decimal point: Make sure to place the decimal point in the correct position, which is determined by the total number of decimal places in the factors.
• Rounding errors: Avoid rounding errors by using a calculator or by following the steps outlined above.
• Not counting the total number of decimal places: Make sure to count the total number of decimal places in the factors to ensure accurate placement of the decimal point in the product.

Conclusion

In conclusion, multiplying decimals is a fundamental operation in mathematics that has numerous applications in real-world scenarios. By following the steps outlined above and avoiding common mistakes, we can accurately multiply decimals and obtain the correct answer.

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Frequently Asked Questions

Q: What is the correct way to multiply decimals?

A: To multiply decimals, you need to multiply the numbers as if they were whole numbers and then place the decimal point in the correct position. The correct placement of the decimal point is determined by the total number of decimal places in the factors.

Q: How do I determine the correct placement of the decimal point?

A: To determine the correct placement of the decimal point, you need to count the total number of decimal places in the factors. Add the number of decimal places in each factor to determine the total number of decimal places. Then, place the decimal point in the product at the correct position, which is determined by the total number of decimal places.

Q: What is the difference between multiplying decimals and multiplying whole numbers?

A: The main difference between multiplying decimals and multiplying whole numbers is the placement of the decimal point. When multiplying whole numbers, you don't need to worry about the decimal point, but when multiplying decimals, you need to place the decimal point in the correct position.

Q: Can I use a calculator to multiply decimals?

A: Yes, you can use a calculator to multiply decimals. However, it's essential to understand the concept of multiplying decimals and how to place the decimal point in the correct position. Using a calculator can help you avoid errors, but it's not a substitute for understanding the concept.

Q: What are some common mistakes to avoid when multiplying decimals?

A: Some common mistakes to avoid when multiplying decimals include:

• Incorrect placement of the decimal point
• Rounding errors
• Not counting the total number of decimal places

Q: How can I practice multiplying decimals?

A: You can practice multiplying decimals by using online resources, such as calculators or multiplication tables. You can also practice by creating your own multiplication problems and solving them.

Q: What are some real-world applications of multiplying decimals?

A: Multiplying decimals has numerous real-world applications, including:

• Finance: Calculating interest rates or investment returns
• Science: Calculating volumes or areas of shapes
• Engineering: Designing and optimizing systems

Q: Can I use a formula to multiply decimals?

A: Yes, you can use a formula to multiply decimals. The formula is:

(a × b) × c = a × (b × c)

Where a, b, and c are the factors being multiplied.

Q: What is the order of operations when multiplying decimals?

A: The order of operations when multiplying decimals is:

1. Multiply the numbers as if they were whole numbers
2. Count the total number of decimal places in the factors
3. Place the decimal point in the product at the correct position

Q: Can I multiply decimals with negative numbers?

A: Yes, you can multiply decimals with negative numbers. When multiplying decimals with negative numbers, you need to follow the same steps as when multiplying decimals with positive numbers, but you also need to consider the sign of the product.

Q: What are some tips for multiplying decimals quickly and accurately?

A: Some tips for multiplying decimals quickly and accurately include:

• Using a calculator
• Lining up the decimal points
• Checking your work
• Practicing regularly

Conclusion

In conclusion, multiplying decimals is a fundamental operation in mathematics that has numerous applications in real-world scenarios. By understanding the concept of multiplying decimals and following the steps outlined above, you can accurately multiply decimals and obtain the correct answer.