The population of a city is given as 3.45 x 10% A nearby city has a population of 1.3 × 105 What is the sum of the populations of the two cities in scientific notation? (1 point)
O 35.8 + 105
• 4.75 x 105
• 3.58 × 108
• 4.75 x 1011
To find the sum of the populations of the two cities, we need to add the values together.
The population of the first city is given as 3.45 x 10^5 (in scientific notation).
The population of the second city is given as 1.3 x 10^5 (in scientific notation).
To add these together, we need to ensure that the powers of 10 are the same. We can do this by converting the population of the second city to scientific notation:
1.3 x 10^5 = 13 x 10^4
Now that both values are in scientific notation, we can add them together:
3.45 x 10^5 + 13 x 10^4 = 3.45 x 10^5 + 0.13 x 10^6
To add these, we first need to make the powers of 10 the same:
3.45 x 10^5 + 0.13 x 10^6 = 3.45 x 10^5 + 1.3 x 10^5
Now, we can add the coefficients:
3.45 + 1.3 = 4.75
Finally, we can write the sum in scientific notation:
4.75 x 10^5
Therefore, the sum of the populations of the two cities is 4.75 x 10^5. So, the correct answer is the option "4.75 x 10^5".
To find the sum of the populations of the two cities in scientific notation, we can first express each population in standard form and then add them together.
The population of the first city is given as 3.45 x 10%, which can be written as 3.45 x 10^-2 because the exponent represents the number of decimal places we need to move the decimal point to the left. Therefore, the population of the first city is 0.0345.
The population of the second city is given as 1.3 × 105, which is already in standard form.
Now, we can add the populations together:
0.0345 + 1.3 × 10^5
To add these two numbers together, we need to make sure they have the same exponent. We can convert 0.0345 to scientific notation by moving the decimal point two places to the right, resulting in 3.45 x 10^-2.
3.45 x 10^-2 + 1.3 × 10^5
Now that they have the same exponent, we can add the numbers:
3.45 x 10^-2 + 1.3 × 10^5 = 1.3 × 10^5 + 3.45 x 10^-2 = 1.3000345 x 10^5
However, for scientific notation, we need to express the number as a decimal between 1 and 10. To do this, we can move the decimal point to the left once, resulting in:
13.000345 x 10^4
This is equivalent to 1.3000345 x 10^5, maintaining the same value.
Therefore, the sum of the populations of the two cities in scientific notation is 1.3000345 x 10^5.
However, none of the answer choices match this result. It seems there may be a mistake in the options provided.
To find the sum of the populations of the two cities in scientific notation, first, convert the population of the first city to scientific notation.
The population of the first city is given as 3.45 x 10%.
To convert this to scientific notation, we need to move the decimal point one place to the right, so the population in scientific notation becomes 3.45 x 10^1.
Now, write down the population of the nearby city in scientific notation.
The population of the nearby city is given as 1.3 x 10^5.
To find the sum of the populations, add the two populations:
3.45 x 10^1 + 1.3 x 10^5.
To add the populations, the exponents of 10 must be the same.
We can rewrite 3.45 x 10^1 as 34.5 x 10^0.
Now, we can add the populations:
34.5 x 10^0 + 1.3 x 10^5.
Since the exponents are the same, we can just add the coefficients:
34.5 + 1.3 = 35.8.
So, the sum of the populations of the two cities is 35.8 in scientific notation.
Therefore, the correct answer is 35.8 + 10^5.