Question
Question 1
A baseball team played three consecutive home games. The first game was attended by 28,453 people. The second game was attended by 30,678 people. The third game was attended by 24,234 people.
Part A
Explain how you can round to estimate the total number of people that attended the three games.
A baseball team played three consecutive home games. The first game was attended by 28,453 people. The second game was attended by 30,678 people. The third game was attended by 24,234 people.
Part A
Explain how you can round to estimate the total number of people that attended the three games.
Answers
GPT-4o mini
To estimate the total number of people that attended the three games, we can round each attendance figure to the nearest thousand. This simplifies the numbers, making it easier to add them together for a quick estimate. Here’s how rounding would work for each game:
1. **First Game:** 28,453 can be rounded to 28,000 (the hundreds digit is 4, which rounds down).
2. **Second Game:** 30,678 can be rounded to 31,000 (the hundreds digit is 6, which rounds up).
3. **Third Game:** 24,234 can be rounded to 24,000 (the hundreds digit is 2, which rounds down).
Now, we can add these rounded numbers together:
- 28,000 (first game)
- 31,000 (second game)
- 24,000 (third game)
Adding these rounded figures gives:
28,000 + 31,000 + 24,000 = 83,000
So, by rounding to the nearest thousand, we estimate that approximately 83,000 people attended the three games. This method provides a quick way to get a rough idea of the total attendance without dealing with the exact numbers.
1. **First Game:** 28,453 can be rounded to 28,000 (the hundreds digit is 4, which rounds down).
2. **Second Game:** 30,678 can be rounded to 31,000 (the hundreds digit is 6, which rounds up).
3. **Third Game:** 24,234 can be rounded to 24,000 (the hundreds digit is 2, which rounds down).
Now, we can add these rounded numbers together:
- 28,000 (first game)
- 31,000 (second game)
- 24,000 (third game)
Adding these rounded figures gives:
28,000 + 31,000 + 24,000 = 83,000
So, by rounding to the nearest thousand, we estimate that approximately 83,000 people attended the three games. This method provides a quick way to get a rough idea of the total attendance without dealing with the exact numbers.
What is the actual number of people that attended the three games? How can you use the estimate to check if your answer is reasonable?
(1 point)
(1 point)
GPT-4o mini
To find the actual number of people that attended the three games, we simply need to add the actual attendance figures for each game:
1. **First Game:** 28,453
2. **Second Game:** 30,678
3. **Third Game:** 24,234
Now, let's add these three figures together:
\[
28,453 + 30,678 + 24,234
\]
Calculating this step by step:
1. Add the first two numbers:
\[
28,453 + 30,678 = 59,131
\]
2. Now add the third number:
\[
59,131 + 24,234 = 83,365
\]
So, the actual total attendance for the three games is **83,365** people.
### Checking the Reasonableness of the Estimate
Our rounded estimate for the total attendance was approximately **83,000**.
To check if this estimate is reasonable, we can compare it with the actual total attendance:
- Actual total: **83,365**
- Estimated total: **83,000**
Since **83,365** is very close to **83,000** (within 365 people), we can conclude that the estimate is reasonable. The estimate provided a quick and close approximation of the actual attendance. This confirmation indicates that our rounding and estimation method was effective.
1. **First Game:** 28,453
2. **Second Game:** 30,678
3. **Third Game:** 24,234
Now, let's add these three figures together:
\[
28,453 + 30,678 + 24,234
\]
Calculating this step by step:
1. Add the first two numbers:
\[
28,453 + 30,678 = 59,131
\]
2. Now add the third number:
\[
59,131 + 24,234 = 83,365
\]
So, the actual total attendance for the three games is **83,365** people.
### Checking the Reasonableness of the Estimate
Our rounded estimate for the total attendance was approximately **83,000**.
To check if this estimate is reasonable, we can compare it with the actual total attendance:
- Actual total: **83,365**
- Estimated total: **83,000**
Since **83,365** is very close to **83,000** (within 365 people), we can conclude that the estimate is reasonable. The estimate provided a quick and close approximation of the actual attendance. This confirmation indicates that our rounding and estimation method was effective.