To simplify this expression, you can add the numbers in front of the powers of 10 and keep the same power of 10.
2.25 × 10⁴ + 3.5 × 10⁵ = (2.25 + 3.5) × 10⁵
Simplifying the numbers in front of the powers of 10:
2.25 + 3.5 = 5.75
So the simplified expression is:
5.75 × 10⁵
2.25 × 10⁴ + 3.5 × 10⁵
5 answers
Can you explain further?
Apologies for the confusion. Let's start from the beginning:
To add numbers in scientific notation, we need to have the same exponent (power of 10). In this case, we have:
2.25 × 10⁴ and 3.5 × 10⁵
First, let's make sure they have the same exponent. We can rewrite the number 2.25 × 10⁴ in scientific notation with an exponent of 5:
2.25 × 10⁴ = 0.225 × 10⁵
To convert 2.25 to 0.225, we need to move the decimal point one place to the left, which increases the exponent by 1.
Now we have:
0.225 × 10⁵ and 3.5 × 10⁵
Since they both have the same exponent (5), we can add the numbers in front:
0.225 + 3.5 = 3.725
So the sum is 3.725 × 10⁵.
To add numbers in scientific notation, we need to have the same exponent (power of 10). In this case, we have:
2.25 × 10⁴ and 3.5 × 10⁵
First, let's make sure they have the same exponent. We can rewrite the number 2.25 × 10⁴ in scientific notation with an exponent of 5:
2.25 × 10⁴ = 0.225 × 10⁵
To convert 2.25 to 0.225, we need to move the decimal point one place to the left, which increases the exponent by 1.
Now we have:
0.225 × 10⁵ and 3.5 × 10⁵
Since they both have the same exponent (5), we can add the numbers in front:
0.225 + 3.5 = 3.725
So the sum is 3.725 × 10⁵.
The combined volume of all the tanks at an aquarium is 2.25 × 10⁴ gallons. The aquarium plans to install a new dolphin tank with a volume of 350,000 gallons. What will be the total volume of all the tanks at the aquarium after the new dolphin tank is installed?
A. 5.75 × 10⁴
B. 5.75 × 10⁵
C. 3.725 × 10⁴
D. 3.725 × 10⁵
A. 5.75 × 10⁴
B. 5.75 × 10⁵
C. 3.725 × 10⁴
D. 3.725 × 10⁵
To find the total volume of all the tanks at the aquarium after the new dolphin tank is installed, we need to add the volume of the new dolphin tank to the existing combined volume of the other tanks.
The combined volume of all the tanks before installing the new dolphin tank is 2.25 × 10⁴ gallons.
The volume of the new dolphin tank is 350,000 gallons, given as 3.5 × 10⁵ in scientific notation.
To add these volumes together, we need to rewrite the combined volume of the other tanks to have the same exponent as the volume of the dolphin tank:
2.25 × 10⁴ = 0.225 × 10⁵ (moving the decimal point one place to the left)
Now we can add the volumes:
0.225 × 10⁵ + 3.5 × 10⁵ = (0.225 + 3.5) × 10⁵
Simplifying the addition:
0.225 + 3.5 = 3.725
Therefore, the total volume of all the tanks after installing the new dolphin tank is 3.725 × 10⁵.
So, the answer is D. 3.725 × 10⁵.
The combined volume of all the tanks before installing the new dolphin tank is 2.25 × 10⁴ gallons.
The volume of the new dolphin tank is 350,000 gallons, given as 3.5 × 10⁵ in scientific notation.
To add these volumes together, we need to rewrite the combined volume of the other tanks to have the same exponent as the volume of the dolphin tank:
2.25 × 10⁴ = 0.225 × 10⁵ (moving the decimal point one place to the left)
Now we can add the volumes:
0.225 × 10⁵ + 3.5 × 10⁵ = (0.225 + 3.5) × 10⁵
Simplifying the addition:
0.225 + 3.5 = 3.725
Therefore, the total volume of all the tanks after installing the new dolphin tank is 3.725 × 10⁵.
So, the answer is D. 3.725 × 10⁵.