A: Distances from planets to the sun in scientific notation:
- Mercury: 5.79 x 10^7 km
- Venus: 1.08 x 10^8 km
- Earth: 1.50 x 10^8 km
- Mars: 2.28 x 10^8 km
- Jupiter: 7.78 x 10^8 km
- Saturn: 1.43 x 10^9 km
- Uranus: 2.87 x 10^9 km
- Neptune: 4.50 x 10^9 km
Since there is no shortest and longest distance in this case, we can simply use the average distance from the sun, which is approximately 2.87 x 10^9 km.
B: Choosing distances from Mars and Neptune:
Distance from Mars: 2.28 x 10^8 km
Distance from Neptune: 4.50 x 10^9 km
Adding the distances: (2.28 x 10^8 km) + (4.50 x 10^9 km) = 4.73 x 10^9 km
C: Choosing distances from Venus and Mercury:
Distance from Venus: 1.08 x 10^8 km
Distance from Mercury: 5.79 x 10^7 km
Subtracting the distances: (1.08 x 10^8 km) - (5.79 x 10^7 km) = 5.0 x 10^7 km
D: Choosing distances from Earth and Saturn:
Distance from Earth: 1.50 x 10^8 km
Distance from Saturn: 1.43 x 10^9 km
Multiplying the distances: (1.50 x 10^8 km) * (1.43 x 10^9 km) = 2.15 x 10^17 km^2
E: Choosing distances from Jupiter and Uranus:
Distance from Jupiter: 7.78 x 10^8 km
Distance from Uranus: 2.87 x 10^9 km
Dividing the distances: (7.78 x 10^8 km) / (2.87 x 10^9 km) = 0.27
4: When adding or subtracting numbers written in scientific notation, we need to ensure that the exponents are the same. We can then perform the addition or subtraction on the coefficients while keeping the same exponent. When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents. When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents.
The steps involved in each case are similar as we need to rearrange the numbers to ensure the exponents are the same and then perform the operation on the coefficients. However, the operations and the ways in which we manipulate the exponents differ.
Adding or subtracting numbers written in scientific notation is generally easier as we only need to adjust the exponents and perform addition or subtraction on the coefficients. Multiplying or dividing numbers written in scientific notation involves both multiplication or division of the coefficients and manipulation of the exponents, which can be more complex.
A:Make a list of the distances from each planet to the sun, written in scientific notation. If there is a shortest and longest distance, use the average distance from the sun.
B:Choose two of the distances of planets from the sun and add them. Show your work.
C:Choose two of the distances of planets from the sun and subtract them. Show your work.
D:Choose two of the distances of planets from the sun and multiply them. Show your work.
E:Choose two of the distances of planets from the sun and divide them. Show your work
4:Compare and contrast adding/subtracting numbers written in scientific notation with multiplying/dividing numbers written in scientific notation. How are the steps in each case similar? How are they different? Do you think adding, subtracting, multiplying, or dividing numbers written in scientific notation is easiest? Why?
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