Solve The Following Multiplication, Rounding Each Number To The Specified Decimal Places:1.93 (rounded To 2 Decimal Places) × 5.4 (rounded To 1 Decimal Place)
Introduction
In mathematics, multiplication is a fundamental operation that involves the repeated addition of a number. However, when dealing with decimal numbers, it's essential to round them to the specified decimal places before performing the multiplication. In this article, we'll explore how to solve the multiplication problem 1.93 (rounded to 2 decimal places) × 5.4 (rounded to 1 decimal place).
Rounding Numbers to Specified Decimal Places
Before we proceed with the multiplication, let's understand how to round numbers to specified decimal places. Rounding a number to a specific decimal place involves looking at the digit immediately to the right of the specified decimal place and deciding whether to round up or down.
- Rounding up: If the digit to the right of the specified decimal place is 5 or greater, we round up the digit at the specified decimal place.
- Rounding down: If the digit to the right of the specified decimal place is less than 5, we round down the digit at the specified decimal place.
Rounding 1.93 to 2 Decimal Places
To round 1.93 to 2 decimal places, we look at the digit to the right of the 2nd decimal place, which is 3. Since 3 is less than 5, we round down the digit at the 2nd decimal place, resulting in 1.9.
Rounding 5.4 to 1 Decimal Place
To round 5.4 to 1 decimal place, we look at the digit to the right of the 1st decimal place, which is 4. Since 4 is less than 5, we round down the digit at the 1st decimal place, resulting in 5.4.
Multiplication with Rounded Numbers
Now that we've rounded the numbers to the specified decimal places, we can proceed with the multiplication.
1.93 (rounded to 2 decimal places) × 5.4 (rounded to 1 decimal place) = ?
To solve this multiplication problem, we can use the distributive property of multiplication over addition. We can break down the multiplication into smaller parts and then combine the results.
1.93 × 5 = 9.65 1.93 × 0.4 = 0.772
Now, we add the results of the two multiplications:
9.65 + 0.772 = 10.422
Rounding the Result
Since we're asked to round the result to the specified decimal places, we need to round 10.422 to 2 decimal places. Looking at the digit to the right of the 2nd decimal place, which is 2, we round down the digit at the 2nd decimal place, resulting in 10.42.
Conclusion
In this article, we've explored how to solve the multiplication problem 1.93 (rounded to 2 decimal places) × 5.4 (rounded to 1 decimal place). We've learned how to round numbers to specified decimal places and then applied this knowledge to the multiplication problem. By breaking down the multiplication into smaller parts and combining the results, we arrived at the final answer of 10.42.
Real-World Applications
Rounding numbers to specified decimal places is a crucial skill in various real-world applications, such as:
- Finance: When dealing with financial transactions, it's essential to round numbers to the specified decimal places to avoid errors.
- Science: In scientific calculations, rounding numbers to specified decimal places helps to simplify complex calculations and avoid errors.
- Engineering: In engineering applications, rounding numbers to specified decimal places is crucial for designing and building structures, machines, and systems.
Practice Problems
To reinforce your understanding of rounding numbers to specified decimal places and multiplication with rounded numbers, try the following practice problems:
- 2.17 (rounded to 2 decimal places) × 3.2 (rounded to 1 decimal place)
- 4.93 (rounded to 2 decimal places) × 2.5 (rounded to 1 decimal place)
Q: What is the importance of rounding numbers to specified decimal places in multiplication?
A: Rounding numbers to specified decimal places is crucial in multiplication because it helps to simplify complex calculations and avoid errors. By rounding numbers to the specified decimal places, we can reduce the number of decimal places in the result, making it easier to work with.
Q: How do I round a number to a specified decimal place?
A: To round a number to a specified decimal place, look at the digit to the right of the specified decimal place. If the digit is 5 or greater, round up the digit at the specified decimal place. If the digit is less than 5, round down the digit at the specified decimal place.
Q: What is the distributive property of multiplication over addition?
A: The distributive property of multiplication over addition is a mathematical property that allows us to break down a multiplication problem into smaller parts and then combine the results. It states that a(b + c) = ab + ac.
Q: How do I apply the distributive property of multiplication over addition to a multiplication problem?
A: To apply the distributive property of multiplication over addition to a multiplication problem, break down the multiplication into smaller parts and then combine the results. For example, in the problem 1.93 (rounded to 2 decimal places) × 5.4 (rounded to 1 decimal place), we can break down the multiplication into 1.93 × 5 and 1.93 × 0.4, and then combine the results.
Q: What is the final answer to the problem 1.93 (rounded to 2 decimal places) × 5.4 (rounded to 1 decimal place)?
A: The final answer to the problem 1.93 (rounded to 2 decimal places) × 5.4 (rounded to 1 decimal place) is 10.42.
Q: What are some real-world applications of rounding numbers to specified decimal places and multiplication with rounded numbers?
A: Some real-world applications of rounding numbers to specified decimal places and multiplication with rounded numbers include finance, science, and engineering. In finance, rounding numbers to specified decimal places helps to avoid errors in financial transactions. In science, rounding numbers to specified decimal places helps to simplify complex calculations. In engineering, rounding numbers to specified decimal places is crucial for designing and building structures, machines, and systems.
Q: How can I practice rounding numbers to specified decimal places and multiplication with rounded numbers?
A: You can practice rounding numbers to specified decimal places and multiplication with rounded numbers by trying the following practice problems:
- 2.17 (rounded to 2 decimal places) × 3.2 (rounded to 1 decimal place)
- 4.93 (rounded to 2 decimal places) × 2.5 (rounded to 1 decimal place)
By practicing these problems, you'll become more confident in your ability to round numbers to specified decimal places and perform multiplication with rounded numbers.
Q: What are some common mistakes to avoid when rounding numbers to specified decimal places and performing multiplication with rounded numbers?
A: Some common mistakes to avoid when rounding numbers to specified decimal places and performing multiplication with rounded numbers include:
- Rounding numbers incorrectly
- Failing to round numbers to the specified decimal places
- Not applying the distributive property of multiplication over addition correctly
- Not combining the results of the multiplication correctly
By avoiding these common mistakes, you'll be able to accurately round numbers to specified decimal places and perform multiplication with rounded numbers.