- Rounding rules: If the ones digit is less than 5, round down; if 5 or greater, round up.
- Vegetable weights rounded: Carrot = \(60\text{ g}\), Hot Pepper = \(10\text{ g}\), Beet = \(90\text{ g}\).
- Estimations: Combined weight of carrot and hot pepper is \(60+10 = 70\text{ g}\); difference between beet and hot pepper is \(90-10 = 80\text{ g}\), making Ray's claim of \(75\text{ g}\) reasonable.
- Measurement estimations: \(252 - 147 \approx 250 - 150 = 100\text{ cm}\); \(418 + 566 \approx 420 + 570 = 990\text{ L}\).
- Final answers: \(\boxed{70\text{ g}, 80\text{ g}, \text{Yes}, 100\text{ cm}, 990\text{ L}}\)
Explanation
- Rounding Vegetable Weights
Rounding numbers to the nearest ten involves looking at the digit in the ones place. If the digit in the ones place is \(0, 1, 2, 3, \text{ or } 4\), we round down by keeping the tens digit the same and changing the ones digit to \(0\). If the digit in the ones place is \(5, 6, 7, 8, \text{ or } 9\), we round up by increasing the tens digit by \(1\) and changing the ones digit to \(0\).
For the vegetable weights:
- Carrot: The weight is \(64\). Since the ones digit \(4\) is less than \(5\), we round down to \(60\text{ g}\).
- Hot Pepper: The weight is \(13\). Since the ones digit \(3\) is less than \(5\), we round down to \(10\text{ g}\).
- Beet: The weight is \(88\). Since the ones digit \(8\) is greater than or equal to \(5\), we round up to \(90\text{ g}\).
| Vegetable | Weight of Vegetable (grams) | Weight Rounded to the Nearest Ten (grams) |
| :--- | :--- | :--- |
| Carrot | \(64\) | \(60\) |
| Hot Pepper | \(13\) | \(10\) |
| Beet | \(88\) | \(90\) |
- Estimation of Vegetable Weights
ATo estimate the combined weight of the carrot and the hot pepper, we add their rounded weights: \(60\text{ g} + 10\text{ g} = 70\text{ g}\).
BTo estimate how much more the beet weighs than the hot pepper, we subtract the rounded weight of the hot pepper from the rounded weight of the beet: \(90\text{ g} - 10\text{ g} = 80\text{ g}\).
CRay says that the beet weighs \(75\text{ g}\) more than the hot pepper. Since our estimation using the rounded values is \(80\text{ g}\), which is very close to \(75\text{ g}\), Ray's claim is reasonable. Estimation by rounding is a helpful way to check if a value makes sense.
- Estimation of Measurements
- For the calculation \(252\text{ cm} - 147\text{ cm}\):
- Round \(252\) to the nearest ten: \(250\).
- Round \(147\) to the nearest ten: \(150\).
- Subtract the rounded values: \(250 - 150 = 100\). The estimated difference is \(100\text{ cm}\).
- For the calculation \(418\text{ L} + 566\text{ L}\):
- Round \(418\) to the nearest ten: \(420\).
- Round \(566\) to the nearest ten: \(570\).
- Add the rounded values: \(420 + 570 = 990\). The estimated sum is \(990\text{ L}\).
Examples
Rounding to the nearest ten is a common skill used in daily life when precise numbers are not required. For instance, if you are shopping and want to quickly estimate the total cost of your items, you might round each price to the nearest dollar or ten dollars. Similarly, when measuring ingredients for a large batch of cooking, rounding to a convenient unit helps in making quick decisions while keeping the overall result close to the actual value, ensuring your final dish remains balanced and flavorful.