Sure, let's go through the problem step-by-step.
We need to determine if the product of [tex]\(22.8 \times 4.7\)[/tex] equals the estimated value of 107.16 and assess if the estimate is reasonable.
### Step-by-Step Solution:
Step 1: Understand the Problem
- You are given two numbers: 22.8 and 4.7.
- You need to multiply these two numbers.
- You have an estimated product: 107.16.
- We need to check if this estimate is reasonable.
Step 2: Perform the Multiplication
When we multiply the exact values:
[tex]\[ 22.8 \times 4.7 = 107.16000000000001 \][/tex]
Step 3: Compare the Actual Product with the Estimate
- The exact product we calculated is 107.16000000000001.
- The estimated product given is 107.16.
Step 4: Assess the Reasonableness
- The exact product (107.16000000000001) is very close to the estimated value of 107.16.
- Therefore, the estimate is almost equivalent to the actual result, suggesting that the estimation is highly accurate.
Conclusion:
Since the real product (107.16000000000001) is just a tiny bit more than the estimate (107.16) and the difference is negligible, the given estimate can be considered reasonable.
Answer: Yes, the estimate of 107.16 is reasonable.
