Will rounding to the nearest 10th or the nearest hundred give a closer estimate of 748-431?
explain your answer.
Rounding to the nearest 10th and rounding to the nearest hundred will not give a closer estimate of 748-431.
When rounding to the nearest 10th, we consider the digit in the hundredth place. In this case, the digit in the hundredth place is 4, which is less than 5. So, when rounding to the nearest 10th, we round down to 740.
When rounding to the nearest hundred, we consider the digit in the tens place. In this case, the digit in the tens place is 4, which is less than 5. So, when rounding to the nearest hundred, we also round down to 700.
Neither of these approximations (740 or 700) is closer to the actual value of 748-431, which is 317. So, rounding to the nearest 10th or the nearest hundred does not provide a closer estimate of the subtraction.
To determine which rounding method will give a closer estimate of the subtraction 748 - 431, we need to consider the magnitudes of the numbers involved.
The number 748 is closer to 700 than it is to 800.
Similarly, the number 431 is closer to 400 than it is to 500.
Now, let's consider rounding to the nearest 10th:
748 rounded to the nearest 10th is 750.
431 rounded to the nearest 10th is 430.
Using these rounded numbers, the subtraction becomes: 750 - 430 = 320.
Now, let's consider rounding to the nearest hundred:
748 rounded to the nearest hundred is 700.
431 rounded to the nearest hundred is 400.
Using these rounded numbers, the subtraction becomes: 700 - 400 = 300.
Comparing the two results, we can see that rounding to the nearest 10th (320) is a closer estimate of the actual subtraction 748 - 431 than rounding to the nearest hundred (300).
Therefore, rounding to the nearest 10th gives a closer estimate of the subtraction 748 - 431.
To determine which rounding method – nearest 10th or nearest hundred – will give a closer estimate of 748 - 431, we need to understand what each method does.
Rounding to the nearest 10th involves looking at the digit in the hundredth position. If the digit is 5 or greater, we round up to the next 10th. If the digit is 4 or less, we round down to the current 10th.
Rounding to the nearest hundred involves looking at the digit in the tens position. If the digit in the ones position is 5 or greater, we round up to the next hundred. If the digit in the ones position is 4 or less, we round down to the current hundred.
Now let's apply these rounding methods to the subtraction 748 - 431.
To round to the nearest 10th:
1. First, round each number to the nearest 10th:
- 748 becomes 750 (rounding up)
- 431 remains 431 (no rounding needed)
2. Subtract the rounded numbers: 750 - 431 = 319
To round to the nearest hundred:
1. First, round each number to the nearest hundred:
- 748 becomes 700 (rounding down)
- 431 remains 431 (no rounding needed)
2. Subtract the rounded numbers: 700 - 431 = 269
In this case, rounding to the nearest 10th (319) is a closer estimate of 748 - 431 compared to rounding to the nearest hundred (269). Rounding to the nearest 10th is more precise because it takes into account the individual digits, while rounding to the nearest hundred only considers the tens digit.