A water park has pools, slides, and rides that, in total, make use of 6, point, 9, times, 10, to the power 56.9×10
5
gallons of water. They plan to add a ride that would make use of an additional 83, comma, 00083,000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
To express the total gallons of water made use of in the park after the new ride is installed, we need to add the additional 83,000 gallons of water to the initial amount of water used in scientific notation.
The initial amount of water used is 6.9 × 10^56.9 × 10^5 gallons.
Adding 83,000 gallons to this amount gives us 6.9 × 10^56.9 × 10^5 + 83,000 gallons.
Using the rule of scientific notation, we can rewrite 83,000 as 8.3 × 10^4.
So, the expression for the total gallons of water used in the park after the new ride is installed in scientific notation is 6.9 × 10^56.9 × 10^5 + 8.3 × 10^4 gallons.
Now, we need to simplify this expression.
Multiplying 6.9 × 10^56.9 × 10^5 by 10^4, we get (6.9 × 10^56.9 × 10^5) × (10^4) = 6.9 × 10^56.9 × 10^5+4 = 6.9 × 10^56.9 × 10^9.
Therefore, the total gallons of water used in the park after the new ride is installed in scientific notation is 6.9 × 10^56.9 × 10^9 gallons.
The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method:
Cell G: 7, point, 8, 6, times, 10, to the power minus 27.86×10
−2
centimeters
Cell H: 4, point, 4, 6, times, 10, to the power minus 34.46×10
−3
centimeters
How many times larger is the diameter of cell G than the diameter of cell H? Write your answer in standard notation, rounding to the nearest tenth.
To find how many times larger the diameter of cell G is than the diameter of cell H, we need to divide the diameter of cell G by the diameter of cell H.
The diameter of cell G is given as 7.86 × 10^-2 centimeters.
The diameter of cell H is given as 4.46 × 10^-3 centimeters.
To divide the diameter of cell G by the diameter of cell H, we can divide the coefficients and subtract the exponents of their powers of 10.
So, (7.86 × 10^-2) / (4.46 × 10^-3) = (7.86 / 4.46) × 10^(-2 - (-3)) = 1.761436 × 10^1
Rounding this answer to the nearest tenth, we have 1.8 × 10^1.
Therefore, the diameter of cell G is approximately 18 times larger than the diameter of cell H.
pls try again
Apologies for the previous incorrect response.
To find how many times larger the diameter of cell G is than the diameter of cell H, we need to divide the diameter of cell G by the diameter of cell H.
The diameter of cell G is given as 7.86 × 10^-2 centimeters.
The diameter of cell H is given as 4.46 × 10^-3 centimeters.
To divide the diameter of cell G by the diameter of cell H, we can divide the coefficients and subtract the exponents of their powers of 10.
So, (7.86 × 10^-2) / (4.46 × 10^-3) = (7.86 / 4.46) × (10^-2 - (-3)) = 1.759928 × 10^(3+2) = 1.759928 × 10^5
Rounding this answer to the nearest tenth, we have 1.8 × 10^5.
Therefore, the diameter of cell G is approximately 180,000 times larger than the diameter of cell H.
The approximate areas of Texas and Washington, D.C. are listed below:
Texas: 6, point, 9, 6, times, 10, to the power 56.96×10
5
square kilometers
Washington, D.C.: 1, point, 7, 7, times, 10, squared1.77×10
2
square kilometers
How many times larger is Texas than Washington, D.C.? Write your answer in standard notation, rounding to the nearest tenth.
Answer
Attempt 1 out of 2
Answer:
To find how many times larger Texas is than Washington, D.C., we need to divide the area of Texas by the area of Washington, D.C.
The area of Texas is given as 6.96 × 10^5 square kilometers.
The area of Washington, D.C. is given as 1.77 × 10^2 square kilometers.
To divide the area of Texas by the area of Washington, D.C., we can divide the coefficients and subtract the exponents of their powers of 10.
So, (6.96 × 10^5) / (1.77 × 10^2) = (6.96 / 1.77) × (10^5 - 2) = 3.932203 × 10^(5-2) = 3.932203 × 10^3
Rounding this answer to the nearest tenth, we have 3.9 × 10^3.
Therefore, Texas is approximately 3,900 times larger than Washington, D.C.
Pls give me the correct answer
Apologies for the previous incorrect response.
To find how many times larger Texas is than Washington, D.C., we need to divide the area of Texas by the area of Washington, D.C.
The area of Texas is given as 6.96 × 10^5 square kilometers.
The area of Washington, D.C. is given as 1.77 × 10^2 square kilometers.
To divide the area of Texas by the area of Washington, D.C., we can divide the coefficients and subtract the exponents of their powers of 10.
So, (6.96 × 10^5) / (1.77 × 10^2) = (6.96 / 1.77) × (10^5 - 2) = 3.932203 × 10^(5-2) = 3.932203 × 10^3
Rounding this answer to the nearest tenth, we have 3.9 × 10^3.
Therefore, Texas is approximately 3,900 times larger than Washington, D.C.