Find (2 × 107) + (3 × 104).
A) 2.003 × 104
B) 2.003 × 107
C) 2.03 × 104
D) 2.03 × 107

We have 10 to the 7th in one term and 10 to the 4th in the other term. We need to break up the 10 to the 7th into a power that matches the smaller one. 10^7 = 10^4*10^3 since, when we have like bases (which we do; it's 10), we add the exponents together. Rewriting our original in terms of that like power:

(2 × 10⁴ × 10³) + (3 × 10⁴)

We can now factor out the 10⁴ since it is common in both sets of parenthesis to get:

10⁴(2 × 10³ + 3)

What's inside that set of parenthesis needs to be expanded now. 2 × 10³ is 2000, and add 3 to that and you get 2003. NOW what we have is

2003 × 10⁴

But that's not in correct scientific notation form, so we need to move the decimal over 3 places to left, adding 3 to the exponent of 4 we already have. That gives us, in the end, finally:

2.003 × 10⁷

Choice B.

Find (2 × 107) + (3 × 104). A) 2.003 × 104 B) 2.003 × 107 C) 2.03 × 104 D) 2.03 × 107

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Find (2 × 107) + (3 × 104).
A) 2.003 × 104
B) 2.003 × 107
C) 2.03 × 104
D) 2.03 × 107