Answer :
To determine which scores could have been Amir's actual score, let's consider the process of rounding to the nearest whole number.
Amir's score was rounded to 98. This means his actual score must be between 97.5 and 98.5. Any number in this range, when rounded to the nearest whole number, will result in 98.
Let's go through each option and check if it falls within this range:
1. 97.84: This number is between 97.5 and 98.5, so when rounded to the nearest whole number, it becomes 98. Thus, it could be Amir's actual score.
2. 98.11: This number is also between 97.5 and 98.5. When rounded, it will also result in 98, so it could be Amir's actual score.
3. 97.31: This number is less than 97.5, so when rounded to the nearest whole number, it becomes 97. Therefore, it cannot be Amir's actual score.
4. 97.28: This number is less than 97.5, so when rounded, it also becomes 97. Hence, it cannot be Amir's actual score.
5. 97.02: This number is below 97.5 and rounds to 97, so it cannot be Amir's actual score.
6. 97.4: This number is less than 97.5, which means it rounds to 97 and cannot be Amir's actual score.
So, the scores that could have been Amir's actual score are 97.84 and 98.11.
Amir's score was rounded to 98. This means his actual score must be between 97.5 and 98.5. Any number in this range, when rounded to the nearest whole number, will result in 98.
Let's go through each option and check if it falls within this range:
1. 97.84: This number is between 97.5 and 98.5, so when rounded to the nearest whole number, it becomes 98. Thus, it could be Amir's actual score.
2. 98.11: This number is also between 97.5 and 98.5. When rounded, it will also result in 98, so it could be Amir's actual score.
3. 97.31: This number is less than 97.5, so when rounded to the nearest whole number, it becomes 97. Therefore, it cannot be Amir's actual score.
4. 97.28: This number is less than 97.5, so when rounded, it also becomes 97. Hence, it cannot be Amir's actual score.
5. 97.02: This number is below 97.5 and rounds to 97, so it cannot be Amir's actual score.
6. 97.4: This number is less than 97.5, which means it rounds to 97 and cannot be Amir's actual score.
So, the scores that could have been Amir's actual score are 97.84 and 98.11.
