Part A

Question

Estimate 1012−38
using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression.

Answer 1

To estimate 1012−38, we can use benchmark values for each number.

First, let's estimate 1012. The nearest benchmark value is 1000, which is 10^3. So we can write 1012 as 10^3 × 1.012.

Next, let's estimate 38. The nearest benchmark value is 40, which is 10 × 4. So we can write 38 as 10 × 3.8.

Now we can substitute these estimations back into the expression:

1012 - 38 ≈ (10^3 × 1.012) - (10 × 3.8)

Simplifying the expression:

≈ 1000 × 1.012 - 10 × 3.8

≈ 1012 - 38

≈ 974

Therefore, the estimated value of 1012−38 using benchmark values is approximately 974.