The approximate areas of Florida and New Hampshire are listed below:
Florida: 1, point, 7, times, 10, to the power 51.7×10
5
square kilometers
New Hampshire: 2, point, 4, 2, times, 10, to the power 42.42×10
4
square kilometers
How much larger is Florida? Express your answer using scientific notation.
Answer
Attempt 1 out of 2
Answer:
times, 10×10
square kilometers
To find out how much larger Florida is than New Hampshire, we need to subtract the area of New Hampshire from the area of Florida.
Florida: 1.7 × 10^51.5 square kilometers
New Hampshire: 2.42 × 10^42.4 square kilometers
To subtract the areas, we need to divide the larger area by the smaller area.
Florida/New Hampshire = (1.7 × 10^51.5) / (2.42 × 10^42.4)
To divide the numbers, we subtract the exponents:
Florida/New Hampshire = (1.7 / 2.42) × 10^(51.5 - 42.4)
= 0.702 × 10^9.1
Scientific notation requires the number before the multiplication sign to be between 1 and 10. Therefore, we divide 0.702 by 10 and multiply the exponent by -1.
Florida/New Hampshire = (0.702 / 10) × 10^(9.1 - 1)
= 0.0702 × 10^8.1
Finally, we write the answer in scientific notation:
Florida/New Hampshire = 7.02 × 10^(-2) × 10^8.1
= 7.02 × 10^(8.1 - 2)
= 7.02 × 10^6.1
So Florida is approximately 7.02 × 10^6.1 times larger than New Hampshire.
The approximate average distances from the sun to Neptune and Mercury are listed below:
Neptune: 4, point, 5, times, 10, to the power 94.5×10
9
kilometers
Mercury: 5, point, 7, 9, times, 10, to the power 75.79×10
7
kilometers
How many times farther from the sun is Neptune? Write your answer in standard notation, rounding to the nearest tenth.
To find out how many times farther from the sun Neptune is compared to Mercury, we need to divide the distance from the sun to Neptune by the distance from the sun to Mercury.
Neptune: 4.5 × 10^94.5 kilometers
Mercury: 5.79 × 10^75.7 kilometers
Dividing these numbers gives us:
Neptune/Mercury = (4.5 × 10^94.5) / (5.79 × 10^75.7)
To divide the numbers, we subtract the exponents:
Neptune/Mercury = (4.5 / 5.79) × 10^(94.5 - 75.7)
= 0.778 × 10^18.8
Since the number before the multiplication sign should be between 1 and 10 in standard notation, we divide 0.778 by 10 and multiply the exponent by -1.
Neptune/Mercury = (0.778 / 10) × 10^(18.8 - 1)
= 0.0778 × 10^17.8
To convert this to standard notation, we simply multiply the number by 10 raised to the power of the exponent:
Neptune/Mercury = 0.0778 × 10^17.8
≈ 7.743 × 10^16
Rounded to the nearest tenth, Neptune is approximately 7.7 × 10^16 times farther from the sun than Mercury.
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.
Answer
Attempt 1 out of 2
Answer:
times, 10×10
gallons
To find the total gallons of water used in the park after the new ride is installed, we need to add the amount of water used by the current pools, slides, and rides to the water used by the new ride.
Current water usage: 6.9 × 10^56.9 gallons
Additional water usage: 83000 gallons
To add these numbers, we need to make sure the exponents are the same. We can convert the additional water usage to scientific notation by moving the decimal point to the right until there is only one digit to the left:
Additional water usage: 8.3 × 10^4.918 gallons
Now we can add the numbers:
Total water usage = (6.9 × 10^56.9) + (8.3 × 10^4.918)
To simplify the calculation, we can adjust the exponents:
Total water usage = (6.9 × 10^56.9) + (0.83 × 10^5.918) × 10^(-1)
Now we can add the numbers and adjust the exponent:
Total water usage = (6.9 + 0.83) × 10^56.9 × 10^(-1+5.918)
= 7.73 × 10^56.9+4.918
= 7.73 × 10^61.818
So the total gallons of water used in the park after the new ride is installed is approximately 7.73 × 10^61.8 gallons.
pls try again
To find how much larger Florida is compared to New Hampshire, we need to subtract the area of New Hampshire from the area of Florida.
The area of Florida is given as 1.7 × 10^5 square kilometers.
The area of New Hampshire is given as 2.42 × 10^4 square kilometers.
To subtract these numbers, we need to ensure that the exponents are the same. In this case, we can multiply the area of New Hampshire by 10 to match the exponent of Florida.
2.42 × 10^4 square kilometers becomes 24.2 × 10^4 square kilometers.
Now we can subtract the area of New Hampshire from Florida:
1.7 × 10^5 - 24.2 × 10^4 = (1.7 - 24.2) × 10^5 = -22.5 × 10^4
The result is -22.5 × 10^4 square kilometers. However, it is customary to express scientific notation with a positive coefficient and a smaller exponent. So we can rewrite it as -2.25 × 10^5 square kilometers.
Therefore, Florida is approximately 2.25 × 10^5 square kilometers larger than New Hampshire.