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Use the given information to complete parts I and II. In your final answer, include all calculations.

Planet Earth has an approximate diameter of 1.2742 · 10 10 millimeters. The sun has a diameter of 1.391 · 10 6 kilometers.

Part I: Given that for every one kilometer there are 1,000,000 millimeters, which unit of measurement should be used to best represent the lengths of the sun and Earth's diameters?

Part II: Approximate how many times greater the sun's diameter is than planet Earth's.

9 answers

To solve the problem, we will go through each part step by step.

Part I:

First, we need to convert the sun's diameter from kilometers to millimeters to have both measurements in the same unit.

  1. Convert Sun's Diameter:

    • The sun's diameter is given as \(1.391 \times 10^6\) kilometers.
    • We know that \(1\) kilometer = \(1,000,000\) millimeters.
    • Therefore, we can convert the sun's diameter to millimeters as follows:

    \[ \text{Sun's diameter in millimeters} = 1.391 \times 10^6 , \text{km} \times 1,000,000 , \text{mm/km} \]

    \[ = 1.391 \times 10^6 \times 10^6 , \text{mm} \]

    \[ = 1.391 \times 10^{12} , \text{mm} \]

  2. Earth's Diameter:

    • The Earth's diameter is already given as \(1.2742 \times 10^{10}\) millimeters.

Since the Earth's diameter is already in millimeters and we converted the sun's diameter to millimeters as well, the best unit of measurement to represent the lengths of the sun and Earth's diameters is millimeters.

Part II:

Now that we have both diameters in millimeters, we can approximate how many times greater the sun's diameter is than planet Earth's.

  1. Calculate the Ratio:

\[ \text{Ratio} = \frac{\text{Sun's diameter}}{\text{Earth's diameter}} = \frac{1.391 \times 10^{12} , \text{mm}}{1.2742 \times 10^{10} , \text{mm}} \]

  1. Perform the Calculation:

\[ \text{Ratio} = \frac{1.391}{1.2742} \times \frac{10^{12}}{10^{10}} = \frac{1.391}{1.2742} \times 10^{2} \]

Calculating the numerical part:

\[ \frac{1.391}{1.2742} \approx 1.0909 \quad (\text{using a calculator}) \]

Now multiply by \(10^2\):

\[ 1.0909 \times 100 \approx 109.09 \]

Thus, the sun's diameter is approximately 109.09 times greater than the Earth's diameter.

Final Answer:

  • Part I: The best unit of measurement for the lengths of the sun and Earth’s diameters is millimeters.
  • Part II: The sun's diameter is approximately 109.09 times greater than planet Earth's diameter.
can you make it less advanced, and not with all the symbols and slashes

Sure! Let’s break it down more simply without using too many symbols or complicated steps.

Part I:

We need to decide which unit of measurement is best to compare the diameters of the Earth and the sun.

  1. Earth’s Diameter: It is given as 12,742,000,000 millimeters (which can be written as 1.2742 x 10^10 mm).

  2. Sun’s Diameter: It is given as 1,391,000 kilometers.

To compare them, we need to convert the sun’s diameter into millimeters.

  • Since 1 kilometer equals 1,000,000 millimeters, we can convert the sun’s diameter:

    • We take the diameter of the sun in kilometers (1,391,000) and multiply it by 1,000,000 to convert it to millimeters.
    • So, 1,391,000 kilometers becomes 1,391,000,000,000 millimeters (or 1.391 x 10^12 mm).

Now both diameters are in millimeters:

  • Earth: 1.2742 x 10^10 mm
  • Sun: 1.391 x 10^12 mm

Since we've converted the sun's diameter to millimeters, the best unit to compare the lengths of the sun and Earth is millimeters.

Part II:

Now, let's find out how many times greater the sun's diameter is compared to Earth's diameter.

  1. We have:

    • Sun's diameter: 1.391 x 10^12 mm
    • Earth’s diameter: 1.2742 x 10^10 mm

  2. Now, to find the ratio:

    • We take the sun’s diameter (1.391 x 10^12) and divide it by the Earth’s diameter (1.2742 x 10^10).

When you do this division, you find that:

  • The sun’s diameter is about 109.09 times greater than the Earth’s diameter.

Final Summary:

  • Part I: The best unit for measurement is millimeters.
  • Part II: The sun's diameter is approximately 109.09 times larger than the Earth's diameter.
can you make it just a little less advanved

Of course! Let’s simplify it even more and use plain language.

Part I:

We need to choose the best unit to compare the sizes of the Earth and the sun.

  1. Earth's Size: The Earth's diameter is 12,742,000,000 millimeters.

  2. Sun's Size: The sun's diameter is 1,391,000 kilometers.

To compare them easily, we should convert the sun's size into millimeters:

  • Since 1 kilometer equals 1,000,000 millimeters, we multiply the sun's diameter by 1,000,000.

So, the sun’s diameter in millimeters is:

1,391,000 km × 1,000,000 mm/km = 1,391,000,000,000 millimeters (or 1.391 trillion mm).

Now we have both sizes in millimeters:

  • Earth's diameter: 12,742,000,000 mm
  • Sun's diameter: 1,391,000,000,000 mm

The best unit to compare both diameters is millimeters.

Part II:

Next, we want to find out how many times bigger the sun is than the Earth.

  1. We know the sizes:

    • Sun's diameter: 1,391,000,000,000 mm
    • Earth’s diameter: 12,742,000,000 mm

  2. To find out how many times bigger the sun is, we divide the sun's diameter by the Earth's diameter:

1,391,000,000,000 mm ÷ 12,742,000,000 mm = about 109.09.

This means the sun is approximately 109 times bigger than the Earth.

Final Summary:

  • Part I: The best unit to measure both sizes is millimeters.
  • Part II: The sun's diameter is about 109 times bigger than the Earth’s diameter.
can you do it with less words

Sure! Here’s a more concise version:

Part I:

  • Earth's Diameter: 12,742,000,000 mm.
  • Sun's Diameter: 1,391,000 km = 1,391,000,000,000 mm (because 1 km = 1,000,000 mm).

Best Unit: Millimeters.

Part II:

  • Sun's Size / Earth's Size:
  • 1,391,000,000,000 mm ÷ 12,742,000,000 mm = about 109.09.

Result: The sun is about 109 times bigger than the Earth.

can you add a little more words to it

Of course! Here’s a slightly more detailed version while still keeping it concise:

Part I:

  • Earth's Diameter: 12,742,000,000 millimeters (mm).
  • Sun's Diameter: 1,391,000 kilometers (km).
    • To compare, we convert this to millimeters: 1,391,000 km is equal to 1,391,000,000,000 mm (since 1 km = 1,000,000 mm).

Conclusion: The best unit to compare both sizes is millimeters.

Part II:

  • To find out how much larger the sun is than the Earth, we divide:
    • Sun’s size (1,391,000,000,000 mm) by Earth’s size (12,742,000,000 mm).

Calculating this gives us about 109.09.

Final Result: The sun is approximately 109 times larger than the Earth.