Question

Interpreting a Solution

Buster was given this expression and asked to determine whether the answer is greater than or less than 1.

(9.763 × 108)(1.56 × 1013)

How can Buster tell without fully performing the calculations?

Buster knows the answer is more than 1, because he can add the exponents to see that the solution will have an exponent of 21.

Buster can tell the answer is less than 1, because he can subtract the exponents to see that the solution will have an exponent of –5.

Buster knows the answer is more than 1, because 9.763 ÷ 1.56 is more than 1.

Buster cannot answer the question without a calculator.

Answer 1

Correct choice: "Buster knows the answer is more than 1, because he can add the exponents to see that the solution will have an exponent of 21."

Reason: when multiplying in scientific notation you add exponents:
(9.763 × 10^8)(1.56 × 10^13) = (9.763×1.56) × 10^(8+13) = (9.763×1.56) × 10^21.
10^21 is already much greater than 1, so the whole product is greater than 1.