Estimate The Sum And The Difference Of The Following By Rounding-off To The Nearest 1,000. A. 3,683 And 2,467 C. 44,046 And 77,781 B. 68,875 And 7,658 D. 1,659 And 50,499​

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Introduction

Rounding off numbers to the nearest 1,000 is a common mathematical operation that helps simplify complex calculations. In this article, we will explore how to estimate the sum and difference of given numbers by rounding them off to the nearest 1,000. We will use real-world examples to illustrate the concept and provide step-by-step solutions.

Rounding Off Numbers

Before we dive into the examples, let's review how to round off numbers to the nearest 1,000. To round off a number to the nearest 1,000, we need to look at the last three digits of the number. If the last three digits are less than 500, we round down to the nearest 1,000. If the last three digits are 500 or more, we round up to the nearest 1,000.

Example 1: Estimating the Sum of 3,683 and 2,467

Let's start with the first example. We need to estimate the sum of 3,683 and 2,467 by rounding them off to the nearest 1,000.

  • Step 1: Round off 3,683 to the nearest 1,000.
    • The last three digits of 3,683 are 683, which is less than 500. Therefore, we round down to 3,000.
  • Step 2: Round off 2,467 to the nearest 1,000.
    • The last three digits of 2,467 are 467, which is less than 500. Therefore, we round down to 2,000.
  • Step 3: Estimate the sum of the rounded numbers.
    • The sum of 3,000 and 2,000 is 5,000.

Therefore, the estimated sum of 3,683 and 2,467 is 5,000.

Example 2: Estimating the Difference of 68,875 and 7,658

Now, let's move on to the second example. We need to estimate the difference of 68,875 and 7,658 by rounding them off to the nearest 1,000.

  • Step 1: Round off 68,875 to the nearest 1,000.
    • The last three digits of 68,875 are 875, which is less than 500. Therefore, we round down to 68,000.
  • Step 2: Round off 7,658 to the nearest 1,000.
    • The last three digits of 7,658 are 658, which is less than 500. Therefore, we round down to 7,000.
  • Step 3: Estimate the difference of the rounded numbers.
    • The difference between 68,000 and 7,000 is 61,000.

Therefore, the estimated difference of 68,875 and 7,658 is 61,000.

Example 3: Estimating the Sum of 44,046 and 77,781

Next, let's consider the third example. We need to estimate the sum of 44,046 and 77,781 by rounding them off to the nearest 1,000.

  • Step 1: Round off 44,046 to the nearest 1,000.
    • The last three digits of 44,046 are 046, which is less than 500. Therefore, we round down to 44,000.
  • Step 2: Round off 77,781 to the nearest 1,000.
    • The last three digits of 77,781 are 781, which is less than 500. Therefore, we round down to 77,000.
  • Step 3: Estimate the sum of the rounded numbers.
    • The sum of 44,000 and 77,000 is 121,000.

Therefore, the estimated sum of 44,046 and 77,781 is 121,000.

Example 4: Estimating the Difference of 1,659 and 50,499

Finally, let's look at the fourth example. We need to estimate the difference of 1,659 and 50,499 by rounding them off to the nearest 1,000.

  • Step 1: Round off 1,659 to the nearest 1,000.
    • The last three digits of 1,659 are 659, which is less than 500. Therefore, we round down to 1,000.
  • Step 2: Round off 50,499 to the nearest 1,000.
    • The last three digits of 50,499 are 499, which is less than 500. Therefore, we round down to 50,000.
  • Step 3: Estimate the difference of the rounded numbers.
    • The difference between 50,000 and 1,000 is 49,000.

Therefore, the estimated difference of 1,659 and 50,499 is 49,000.

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about rounding off numbers to the nearest 1,000.

Q: What is rounding off to the nearest 1,000?

A: Rounding off to the nearest 1,000 is a mathematical operation that involves simplifying a number by rounding it off to the nearest 1,000. This is done by looking at the last three digits of the number and rounding up or down to the nearest 1,000.

Q: How do I round off a number to the nearest 1,000?

A: To round off a number to the nearest 1,000, follow these steps:

  1. Look at the last three digits of the number.
  2. If the last three digits are less than 500, round down to the nearest 1,000.
  3. If the last three digits are 500 or more, round up to the nearest 1,000.

Q: What if the last three digits are exactly 500?

A: If the last three digits are exactly 500, you can round up to the nearest 1,000. For example, if the number is 1,500, you would round up to 2,000.

Q: Can I round off a negative number to the nearest 1,000?

A: Yes, you can round off a negative number to the nearest 1,000. The process is the same as rounding off a positive number. For example, if you have a number like -3,500, you would round it down to -4,000.

Q: How do I estimate the sum of two numbers by rounding them off to the nearest 1,000?

A: To estimate the sum of two numbers by rounding them off to the nearest 1,000, follow these steps:

  1. Round off each number to the nearest 1,000.
  2. Add the rounded numbers together.

Q: How do I estimate the difference of two numbers by rounding them off to the nearest 1,000?

A: To estimate the difference of two numbers by rounding them off to the nearest 1,000, follow these steps:

  1. Round off each number to the nearest 1,000.
  2. Subtract the smaller rounded number from the larger rounded number.

Q: Why is rounding off to the nearest 1,000 useful?

A: Rounding off to the nearest 1,000 is useful because it helps simplify complex calculations and makes it easier to estimate sums and differences. It is also a useful technique for checking the reasonableness of answers.

Q: Can I use rounding off to the nearest 1,000 in real-world applications?

A: Yes, you can use rounding off to the nearest 1,000 in real-world applications. For example, you might use it to estimate the cost of a project, the number of people who will attend an event, or the amount of money that will be spent on a particular item.

Conclusion

In conclusion, rounding off to the nearest 1,000 is a useful mathematical technique that can help simplify complex calculations and make it easier to estimate sums and differences. By following the steps outlined in this article, you can quickly and easily round off numbers to the nearest 1,000 and apply this technique to a wide range of mathematical problems.