Question

Does rounding each number to the nearest ten give an overestimate or an underestimate? Explain.74x11.3

Answer 1

To determine whether rounding each number to the nearest ten gives an overestimate or an underestimate for the product \( 74 \times 11.3 \), we should follow these steps:

1. **Round the Numbers**:
- The number \( 74 \) rounded to the nearest ten is \( 70 \).
- The number \( 11.3 \) rounded to the nearest ten is \( 10 \).

2. **Calculate the Rounded Product**:
- The product of the rounded numbers is \( 70 \times 10 = 700 \).

3. **Calculate the Actual Product**:
- The actual product is \( 74 \times 11.3 = 838.2 \).

4. **Compare the Results**:
- The actual product \( 838.2 \) is greater than the product of the rounded numbers \( 700 \).

Since the product of the rounded numbers \( 700 \) is less than the actual product \( 838.2 \), rounding \( 74 \) to \( 70 \) and \( 11.3 \) to \( 10 \) gives an **underestimate** of the actual product.