Find The Value Of $8.3 \times 24.2 \times 0.03$. Round Your Answer To The Nearest Hundredth.A. 6.03 B. 60.26 C. 79.86 D. 7.99

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Understanding the Problem

When dealing with multiplication of decimal numbers, it's essential to follow the correct order of operations and apply the rules of decimal multiplication. In this problem, we are required to find the value of $8.3 \times 24.2 \times 0.03$ and round the answer to the nearest hundredth.

The Rules of Decimal Multiplication

To multiply decimal numbers, we need to follow the rules of decimal multiplication. The rules are as follows:

  • When multiplying two decimal numbers, we multiply the numbers as if they were whole numbers.
  • We then count the total number of decimal places in the two numbers being multiplied.
  • We place the decimal point in the product at the correct position, which is the total number of decimal places counted in the previous step.

Applying the Rules to the Problem

Let's apply the rules of decimal multiplication to the problem at hand.

Step 1: Multiply the Numbers as if they were Whole Numbers

First, we multiply the numbers as if they were whole numbers.

8.3×24.2×0.03=8.3×24.2×38.3 \times 24.2 \times 0.03 = 8.3 \times 24.2 \times 3

Step 2: Count the Total Number of Decimal Places

Next, we count the total number of decimal places in the numbers being multiplied.

  • The number 8.3 has 1 decimal place.
  • The number 24.2 has 1 decimal place.
  • The number 0.03 has 2 decimal places.

The total number of decimal places is 1 + 1 + 2 = 4.

Step 3: Place the Decimal Point in the Product

Now, we place the decimal point in the product at the correct position, which is 4 decimal places from the right.

8.3×24.2×0.03=6.038.3 \times 24.2 \times 0.03 = 6.03

Rounding the Answer to the Nearest Hundredth

Finally, we round the answer to the nearest hundredth. Since the digit in the thousandths place is less than 5, we round down to 6.03.

Conclusion

In conclusion, the value of $8.3 \times 24.2 \times 0.03$ rounded to the nearest hundredth is 6.03.

Key Takeaways

  • When multiplying decimal numbers, we need to follow the rules of decimal multiplication.
  • We multiply the numbers as if they were whole numbers.
  • We count the total number of decimal places in the numbers being multiplied.
  • We place the decimal point in the product at the correct position.
  • We round the answer to the nearest hundredth.

Practice Problems

Here are some practice problems to help you reinforce your understanding of decimal multiplication.

  • Find the value of $4.5 \times 0.6 \times 0.02$ and round the answer to the nearest hundredth.
  • Find the value of $9.8 \times 3.2 \times 0.05$ and round the answer to the nearest hundredth.
  • Find the value of $2.1 \times 4.5 \times 0.03$ and round the answer to the nearest hundredth.

Solutions to Practice Problems

Here are the solutions to the practice problems.

  • 4.5×0.6×0.02=0.0544.5 \times 0.6 \times 0.02 = 0.054

  • 9.8×3.2×0.05=1.5689.8 \times 3.2 \times 0.05 = 1.568

  • 2.1×4.5×0.03=0.2972.1 \times 4.5 \times 0.03 = 0.297

Conclusion

In conclusion, decimal multiplication is an essential concept in mathematics that requires careful attention to the rules of decimal multiplication. By following the rules and applying them to problems, we can find the correct values of decimal products and round them to the nearest hundredth.

Q: What is decimal multiplication?

A: Decimal multiplication is the process of multiplying two or more decimal numbers to find the product. It involves following the rules of decimal multiplication to ensure that the decimal point is placed in the correct position in the product.

Q: What are the rules of decimal multiplication?

A: The rules of decimal multiplication are as follows:

  • When multiplying two decimal numbers, we multiply the numbers as if they were whole numbers.
  • We then count the total number of decimal places in the two numbers being multiplied.
  • We place the decimal point in the product at the correct position, which is the total number of decimal places counted in the previous step.

Q: How do I multiply decimal numbers?

A: To multiply decimal numbers, follow these steps:

  1. Multiply the numbers as if they were whole numbers.
  2. Count the total number of decimal places in the two numbers being multiplied.
  3. Place the decimal point in the product at the correct position, which is the total number of decimal places counted in the previous step.

Q: What is the importance of decimal multiplication?

A: Decimal multiplication is an essential concept in mathematics that has numerous applications in real-life situations. It is used in various fields such as finance, science, and engineering to perform calculations involving decimal numbers.

Q: How do I round the answer to the nearest hundredth?

A: To round the answer to the nearest hundredth, follow these steps:

  1. Look at the digit in the thousandths place.
  2. If the digit is less than 5, round down to the nearest hundredth.
  3. If the digit is 5 or greater, round up to the nearest hundredth.

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

A: Some common mistakes to avoid when multiplying decimal numbers include:

  • Forgetting to count the total number of decimal places in the two numbers being multiplied.
  • Placing the decimal point in the product at the incorrect position.
  • Not rounding the answer to the nearest hundredth.

Q: How can I practice decimal multiplication?

A: You can practice decimal multiplication by working on problems involving decimal numbers. You can also use online resources and practice tests to help you reinforce your understanding of decimal multiplication.

Q: What are some real-life applications of decimal multiplication?

A: Decimal multiplication has numerous real-life applications, including:

  • Finance: Decimal multiplication is used to calculate interest rates, investment returns, and other financial calculations.
  • Science: Decimal multiplication is used to perform calculations involving scientific measurements and data.
  • Engineering: Decimal multiplication is used to perform calculations involving engineering measurements and data.

Q: How can I improve my understanding of decimal multiplication?

A: You can improve your understanding of decimal multiplication by:

  • Practicing problems involving decimal numbers.
  • Using online resources and practice tests.
  • Seeking help from a teacher or tutor.
  • Reviewing the rules of decimal multiplication and applying them to problems.