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? Choose an answer from below.
35.8 + 10⁵
3.58 × 10⁶
4.75 × 10⁵
4.75 × 10¹¹
To find the sum of the populations of the two cities, we need to add the population of the first city (3.45 × 10⁶) to the population of the second city (1.3 × 10⁵).
To add numbers in scientific notation, we need to make sure the exponents are the same. In this case, we can rewrite the population of the second city as 0.13 × 10⁶ (move the decimal point one place to the left).
Now, we can add the populations:
3.45 × 10⁶ + 0.13 × 10⁶ = 3.58 × 10⁶
Therefore, the sum of the populations of the two cities in scientific notation is 3.58 × 10⁶.
The correct answer is 3.58 × 10⁶.
To find the sum of the populations of the two cities, we need to add the numbers together and represent the result in scientific notation.
The population of the first city is 3.45 × 10⁶, and the population of the second city is 1.3 × 10⁵.
To add these two numbers, we need to align the decimal places. Since the exponent of 10 is higher in the first number (10⁶) compared to the second number (10⁵), we can add them as they are:
3.45 × 10⁶ + 1.3 × 10⁵ = 3.45 × 10⁶ + 0.13 × 10⁶
To add the numbers, we can focus on the coefficients and add them together:
3.45 + 0.13 = 3.58
Now we need to adjust the exponent of 10 by combining the exponents. Since the original exponent of 10 for the first number (10⁶) is higher, we keep it and adjust the coefficient:
3.58 × 10⁶
Therefore, the sum of the populations of the two cities in scientific notation is 3.58 × 10⁶.
Hence, the answer is: 3.58 × 10⁶.
To get the sum of the populations of the two cities in scientific notation, we need to first convert both populations to scientific notation if they aren't already.
The population of the first city is given as 3.45 × 10⁶, which is already in scientific notation.
The population of the second city is given as 1.3 × 10⁵, which is also in scientific notation.
To calculate the sum, we add the values outside of the exponential terms (the coefficients) and keep the base, which in this case is 10, the same:
3.45 × 10⁶ + 1.3 × 10⁵
To add the coefficients, we need to ensure that the exponents are the same. In this case, both numbers have the exponent of 10⁶.
3.45 × 10⁶ + 0.13 × 10⁶ (we divide 1.3 × 10⁵ by 10, moving the decimal one place to the left)
Now, we can add the coefficients:
3.45 + 0.13 = 3.58
The exponent remains the same, so the sum of the populations of the two cities is:
3.58 × 10⁶
Therefore, the correct answer is: 3.58 × 10⁶.