The population of a city is given as 3.45×10 to the power of 6. A nearby city has a population of 1.3×10 to the power of 5? What is the sum of the populations of the two cities in scientific notation?

Answer 1

To find the sum of the populations of the two cities given in scientific notation:

1. The population of the first city is \( 3.45 \times 10^6 \).
2. The population of the second city is \( 1.3 \times 10^5 \).

Before we can add these two numbers, they should be expressed with the same exponent. The larger exponent is \( 10^6 \), so we'll convert the population of the second city to the same exponent:

\[ 1.3 \times 10^5 = 1.3 \times 10^5 \times \frac{10^1}{10^1} = 1.3 \times 10^6 \div 10 = 0.13 \times 10^6 \]

Now we can add the two populations in scientific notation:

\[ 3.45 \times 10^6 + 0.13 \times 10^6 = (3.45 + 0.13) \times 10^6 = 3.58 \times 10^6 \]

Thus, the sum of the populations of the two cities in scientific notation is:

\[ \boxed{3.58 \times 10^6} \]