Question

Which of the following is a correct step in the process of adding 8.0 x 10^ -2 and 6.0 x 10^ -3

The answer is (8.0+0.6)x10^-2, but I was hoping someone could explain how considering one is raised to the second power while one is raised to the third.

Answer 1

Explanation:

In order to compute correctly the sum of the two terms, we have to rewrite one of them such that they have the same exponent.

The two terms are:

$8.0 \cdot 10^{-2}$

$6.0 \cdot 10^{-3}$

For instance, we can re-write the second term such as it also has a power $10^{-2}$. In order to do that, we have to move the decimal point one place to the left, therefore:

$6.0 \cdot 10^{-3} = 0.6\cdot 10^{-2}$

At this point, the two numbers have the same exponent, so we can just add them together by adding the bases and keeping the same exponent, -2:

$8.0\cdot 10^{-2} + 0.6 \cdot 10^{-2} = (8.0 + 0.6) \cdot 10^{-2} = 8.6\cdot 10^{-2}$