Question

the population of a city is given as 3.45 x 10^6 a nearby city has a population of 1.3 x 10^5 what is the sum of the populations of the two cities in scientific notation?

4.75 x 10^11
4.75 x 10^5
3.58 x 10^6
35.8 + 10^5

Answer 1

To find the sum of the populations of the two cities given in scientific notation, we need to express both populations with the same exponent.

The populations are:
- City A: \(3.45 \times 10^6\)
- City B: \(1.3 \times 10^5\)

First, we can convert City B's population to a form that has the same exponent as City A's:

\[
1.3 \times 10^5 = 0.013 \times 10^6
\]

Now, we can add the two populations together:

\[
3.45 \times 10^6 + 0.013 \times 10^6 = (3.45 + 0.013) \times 10^6 = 3.463 \times 10^6
\]

Now, we can check the provided options:
1. \(4.75 \times 10^{11}\)
2. \(4.75 \times 10^{5}\)
3. \(3.58 \times 10^{6}\)
4. \(35.8 + 10^{5}\)

None of these options exactly match \(3.463 \times 10^{6}\) but if we round \(3.463\) to \(3.46\), it's closer to option 3, but it's not exactly there.

Therefore, the answer expressed in scientific notation for the sum of the populations of the two cities is \(3.463 \times 10^6\).