Certainly! Let's go through the steps in estimating the sum of the given numbers and identify which estimate is the closest.
### Step 1: List the given numbers
We have the following numbers:
[tex]\[ 28.71, 29.1, 32.45, 31, 30.9 \][/tex]
### Step 2: Find the exact sum
Let's add these numbers together:
[tex]\[ 28.71 + 29.1 + 32.45 + 31 + 30.9 \][/tex]
By summing these values, we get:
[tex]\[ 28.71 + 29.1 = 57.81 \][/tex]
[tex]\[ 57.81 + 32.45 = 90.26 \][/tex]
[tex]\[ 90.26 + 31 = 121.26 \][/tex]
[tex]\[ 121.26 + 30.9 = 152.16 \][/tex]
Thus, the total sum of these numbers is:
[tex]\[ 152.16 \][/tex]
### Step 3: Determine the closest estimate
Now, we have to compare the sum [tex]\(152.16\)[/tex] with the given estimates:
- 150
- 180
- 130
- 120
Calculate the absolute differences from each estimate:
- Difference with 150 is [tex]\( |152.16 - 150| = 2.16 \)[/tex]
- Difference with 180 is [tex]\( |152.16 - 180| = 27.84 \)[/tex]
- Difference with 130 is [tex]\( |152.16 - 130| = 22.16 \)[/tex]
- Difference with 120 is [tex]\( |152.16 - 120| = 32.16 \)[/tex]
### Step 4: Identify the closest estimate
From the differences calculated:
- [tex]\( 2.16 \)[/tex] with 150
- [tex]\( 27.84 \)[/tex] with 180
- [tex]\( 22.16 \)[/tex] with 130
- [tex]\( 32.16 \)[/tex] with 120
The smallest difference is [tex]\( 2.16 \)[/tex], which corresponds to the estimate of [tex]\( 150 \)[/tex].
### Conclusion
The sum of the given numbers is [tex]\( 152.16 \)[/tex] and the closest estimate to this sum is [tex]\( 150 \)[/tex].
