the population of a city is given as 3.45*10^6. a nearby city has a population of 1.3*10^5. what is the sum of the populations of the two cities in scientific notation
To find the sum of the populations of the two cities in scientific notation, we need to add the two numbers while keeping them in the form of scientific notation.
The population of the first city is given as 3.45 * 10^6.
The population of the second city is given as 1.3 * 10^5.
First, we need to convert the population of the second city to the same power of 10 as the first city so that we can add them together.
To do this, we can express the population of the second city in scientific notation with the same power of 10 as the first city:
1.3 * 10^5 = 0.13 * (10^1) * (10^5) = 0.13 * 10^(1+5) = 0.13 * 10^6.
Now, we can add the two numbers:
3.45 * 10^6 + 0.13 * 10^6 = (3.45 + 0.13) * 10^6 = 3.58 * 10^6.
Therefore, the sum of the populations of the two cities is 3.58 * 10^6.
To find the sum of the populations of the two cities in scientific notation, we need to consider the powers of 10 and perform the addition.
First, let's rewrite the population values in scientific notation:
City A: 3.45 * 10^6
City B: 1.3 * 10^5
To add these values, we need to align the powers of 10:
3.45 * 10^6 + 1.3 * 10^5
To align the powers of 10, we need to convert the population of City B to match the power of 10 of City A. Since City A has 10^6, and City B has 10^5, we can multiply City B's population by 10 to make the powers of 10 equal:
1.3 * 10^5 = 13 * 10^4
Now, we can add the populations using aligned powers of 10:
3.45 * 10^6 + 13 * 10^4 = 3.45 * 10^6 + 0.13 * 10^6
Next, we can combine the coefficients and keep the power of 10:
(3.45 + 0.13) * 10^6 = 3.58 * 10^6
Therefore, the sum of the populations of the two cities in scientific notation is 3.58 * 10^6.
To find the sum of the populations of the two cities in scientific notation, you need to add the numbers part and then adjust the exponent if necessary. Here's how you can do it step by step:
Step 1: Add the numbers part:
3.45 * 10^6 + 1.3 * 10^5
Step 2: Since the exponents (6 and 5) are different, you'll need to adjust them to be the same. To do this, you can rewrite the population of the second city as 0.13 * 10^6. This way, the exponents are the same, and you can add the numbers part:
3.45 * 10^6 + 0.13 * 10^6 = 3.58 * 10^6
Step 3: In scientific notation, we typically write the number so that the numbers part is between 1 and 10. In this case, the sum is already in the correct form (3.58) since it falls within that range. Therefore, the sum of the populations of the two cities in scientific notation is:
3.58 * 10^6