The population of a city is given as 3.45×10⁶. A nearby city has a population of 1.3×10⁵. What is the sum of the populations of the two cities in scientific notation?
The sum of the populations of the two cities can be found by adding the two populations together.
3.45×10⁶ + 1.3×10⁵ = (3.45+1.3)×10⁶ = 4.75×10⁶
So, the sum of the populations of the two cities is 4.75×10⁶.
To find the sum of the populations of the two cities in scientific notation, we need to add the numbers together and express the result in scientific notation.
Step 1: Add the numbers 3.45×10⁶ and 1.3×10⁵.
3.45×10⁶ + 1.3×10⁵ = 3.45×10⁶ + 0.13×10⁶
Step 2: Combine the coefficients.
3.45 + 0.13 = 3.58
Step 3: Keep the common power of 10.
The power of 10 in both numbers is ⁶, so we keep it.
Step 4: Write the sum in scientific notation.
3.58×10⁶
Therefore, the sum of the populations of the two cities in scientific notation is 3.58×10⁶.
To find the sum of the populations of the two cities in scientific notation, we can add the two numbers together and then convert the result to scientific notation if needed.
The population of the first city is 3.45×10⁶.
The population of the second city is 1.3×10⁵.
To add these numbers, we need to make sure they have the same exponent. We can do this by rewriting the population of the second city with an exponent of 6. To do this, we multiply 1.3 by 10 since 10 to the power of 1 is 10:
1.3 × 10 = 13.
So, the population of the second city is 13×10⁵.
Now, we can add the populations of the two cities:
3.45 × 10⁶ + 13 × 10⁵.
To add these numbers, we add the coefficients (3.45 and 13) and keep the same exponent:
3.45 + 13 = 16.45.
Therefore, the sum of the populations of the two cities is 16.45 × 10⁶.
However, this number is not in standard scientific notation form. The coefficient needs to be between 1 and 10. To express it properly, we can divide both the coefficient and the exponent by 10:
16.45 × 10⁶ = 1.645 × 10⁷.
Therefore, the sum of the populations of the two cities in scientific notation is 1.645 × 10⁷.