Question

Which is the best estimate for (1.7 x 1013) + (0.8 x 102)? a. 1.78 x 1012 b. 1.7 x 1013 c. 1.7 x 1014 d. 17.8 x 1014

Answer 1

To find the best estimate for the sum (1.7 x 10^13) + (0.8 x 10^2), we can simplify the terms and perform the addition:

(1.7 x 10^13) + (0.8 x 10^2) = 1.7 x 10^13 + 0.8 x 10^2

To add these two numbers, we need to align the powers of 10:

1.7 x 10^13 + 0.8 x 10^2 = 1.7 x 10^13 + 0.8 x 10^13 x 10^(-11)

Now we have the same exponent for both terms:

1.7 x 10^13 + 0.8 x 10^13 x 10^(-11) = (1.7 + 0.8 x 10^(-11)) x 10^13

The term 0.8 x 10^(-11) is very small compared to 1.7, so we can neglect it for the purpose of estimation. Therefore, the best estimate for the sum is:

(1.7 + 0.8 x 10^(-11)) x 10^13 ≈ 1.7 x 10^13

Thus, the best estimate for the sum (1.7 x 10^13) + (0.8 x 10^2) is option b. 1.7 x 10^13.

Step-by-step explanation: