Find the estimated difference of 43,209 and 3,479 by rounding off to the nearest hundred
The correct answer and explanation is:
Here is the estimated difference and a 300-word explanation:
The correct estimated difference is 39,700.
Explanation:
To find the estimated difference between 43,209 and 3,479 by rounding off to the nearest hundred, we first need to round each number individually according to the specified rule. Estimation is a useful mathematical technique that allows us to quickly find an approximate answer, often simplifying calculations.
The rule for rounding to the nearest hundred involves looking at the digit in the tens place. If this digit is 5 or greater (5, 6, 7, 8, or 9), we round up the hundreds digit by one and change the tens and ones digits to zero. If the tens digit is less than 5 (0, 1, 2, 3, or 4), we keep the hundreds digit as it is and change the tens and ones digits to zero.
First, let’s round the larger number, 43,209, to the nearest hundred. We look at the tens digit, which is 0. Since 0 is less than 5, we keep the hundreds digit, 2, as it is, and replace the tens and ones digits with zeros. So, 43,209 rounded to the nearest hundred becomes 43,200.
Next, we round the smaller number, 3,479, to the nearest hundred. We look at the tens digit, which is 7. Since 7 is 5 or greater, we round up the hundreds digit, 4, to 5, and replace the tens and ones digits with zeros. Thus, 3,479 rounded to the nearest hundred becomes 3,500.
Now that both numbers have been rounded to the nearest hundred, we find their estimated difference by performing the subtraction:
Estimated Difference = Rounded Larger Number – Rounded Smaller Number
Estimated Difference = 43,200 – 3,500
Performing the subtraction:
43,200
- 3,500
39,700
The result of the subtraction of the rounded numbers is 39,700. Therefore, the estimated difference between 43,209 and 3,479, when rounded to the nearest hundred, is 39,700. This estimated value is a good approximation of the actual difference, which would be 39,730.