Multiply.$6.4 \times 31.56$Enter Your Answer In The Box.

$$

Understanding the Problem

When faced with a multiplication problem involving decimal numbers, it's essential to understand the concept of multiplying decimals. Multiplying decimals is similar to multiplying whole numbers, but with an added step to handle the decimal points. In this case, we need to multiply $6.4$ by $31.56$.

Multiplying Decimals

To multiply decimals, we follow these 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 the total number of decimal places counted in step 2.

Step-by-Step Solution

Step 1: Multiply the Numbers as Whole Numbers

First, we multiply $6.4$ by $31.56$ as if they were whole numbers.

6.4 × 31.56 = ?

To multiply these numbers, we can use the standard multiplication algorithm.

  6.4
× 31.56
------
  200.64
+ 201.84
------
  402.48

Step 2: Count the Total Number of Decimal Places

Now, we count the total number of decimal places in the factors.

• $6.4$ has 1 decimal place.
• $31.56$ has 2 decimal places.

The total number of decimal places is $1 + 2 = 3$.

Step 3: Place the Decimal Point

We place the decimal point in the product at the correct position, which is 3 decimal places from the right.

402.48

Final Answer

The final answer is $\boxed{402.48}$.

Conclusion

Multiplying decimals requires understanding the concept of multiplying whole numbers and then adjusting for the decimal points. By following the steps outlined above, we can accurately multiply decimal numbers and obtain the correct result.

Additional Tips

• When multiplying decimals, it's essential to count the total number of decimal places in the factors.
• The decimal point in the product should be placed at the correct position, which is the total number of decimal places counted.
• Multiplying decimals can be simplified by using the standard multiplication algorithm and then adjusting for the decimal points.

Real-World Applications

Multiplying decimals has numerous real-world applications, including:

• Calculating discounts and sales tax
• Determining the cost of materials for a construction project
• Calculating the area and perimeter of a rectangle
• Determining the interest rate on a loan

Practice Problems

Try these practice problems to reinforce your understanding of multiplying decimals:

• $4.2 \times 9.15$
• $2.5 \times 6.8$
• $3.1 \times 4.9$

Common Mistakes

When multiplying decimals, it's common to make mistakes such as:

• Forgetting to count the total number of decimal places
• Placing the decimal point in the wrong position
• Not adjusting for the decimal points when multiplying whole numbers

Conclusion

Multiplying decimals requires attention to detail and a clear understanding of the concept. By following the steps outlined above and practicing with real-world examples, you can become proficient in multiplying decimals and apply this skill to various mathematical problems.

$$

Frequently Asked Questions

Q: What is the concept of multiplying decimals?

A: Multiplying decimals is similar to multiplying whole numbers, but with an added step to handle the decimal points. When multiplying decimals, we need to multiply the numbers as if they were whole numbers and then adjust for the decimal points.

Q: How do I multiply decimals?

A: To multiply decimals, follow these 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 the total number of decimal places counted in step 2.

Q: What if I forget to count the total number of decimal places?

A: If you forget to count the total number of decimal places, your answer will be incorrect. Make sure to count the decimal places carefully and 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 to ensure accuracy.

Q: How do I handle negative numbers when multiplying decimals?

A: When multiplying decimals with negative numbers, follow the same steps as multiplying whole numbers with negative numbers. Remember to count the total number of decimal places and place the decimal point in the correct position.

Q: Can I multiply decimals with fractions?

A: Yes, you can multiply decimals with fractions. To do this, convert the fraction to a decimal and then multiply the decimals.

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

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

• Calculating discounts and sales tax
• Determining the cost of materials for a construction project
• Calculating the area and perimeter of a rectangle
• Determining the interest rate on a loan

Q: How can I practice multiplying decimals?

A: You can practice multiplying decimals by trying the following problems:

• $4.2 \times 9.15$
• $2.5 \times 6.8$
• $3.1 \times 4.9$

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

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

• Forgetting to count the total number of decimal places
• Placing the decimal point in the wrong position
• Not adjusting for the decimal points when multiplying whole numbers

Q: Can I use a multiplication chart to help me multiply decimals?

A: Yes, you can use a multiplication chart to help you multiply decimals. A multiplication chart can help you visualize the multiplication process and ensure accuracy.

Q: How can I apply multiplying decimals to real-world problems?

A: To apply multiplying decimals to real-world problems, follow these steps:

1. Read the problem carefully and identify the numbers to be multiplied.
2. Multiply the numbers as if they were whole numbers.
3. Count the total number of decimal places in the factors.
4. Place the decimal point in the product at the correct position.
5. Check your answer to ensure accuracy.

Conclusion

Multiplying decimals requires attention to detail and a clear understanding of the concept. By following the steps outlined above and practicing with real-world examples, you can become proficient in multiplying decimals and apply this skill to various mathematical problems.