Question

Mario estimated the product of 132.4 × 27.9 in two different ways, as shown below.


Using compatible numbers:

132.4 × 27.9 ≈ 130 × 30 = 3,900


Rounding to the nearst whole number:

132.4 × 27.9 ≈ 132 × 28 = 3,696

Find the exact product. What can you say about Mario’s estimates? Check all that apply.

Answer 1

To find the exact product of 132.4 and 27.9, we can multiply the two numbers together:

\[
132.4 \times 27.9 = 3696.96
\]

Now, let's analyze Mario's estimates:

1. **Using compatible numbers:**
- Mario estimated \( 132.4 \times 27.9 \) as \( 130 \times 30 = 3900 \).
- This estimate is higher than the exact product of 3696.96.

2. **Rounding to the nearest whole number:**
- Mario rounded \( 132.4 \) to \( 132 \) and \( 27.9 \) to \( 28 \) and calculated \( 132 \times 28 = 3696 \).
- This estimate is very close to the exact product, with only 0.96 difference.

### Conclusion about Mario's estimates:
- His first estimate using compatible numbers (3900) was higher than the exact product.
- His second estimate, when rounding to the nearest whole number (3696), was very close, just slightly less than the exact product at 3696.96.

### Summary of observations:
- One estimate (compatible numbers) was significantly higher than the exact product.
- The other estimate (rounding) was very close to the exact product.
- Mario's estimates demonstrated that while compatible numbers can lead to larger discrepancies, rounding can provide a more accurate estimate.