Question

The sun's mass is about 2 × 10³⁰ kilograms, mercury's mass is about 3 × 10²³ kilograms, earth's mass is about 6 × 10²⁴ kilograms, and uranus's mass is about 9 × 10²⁵ kilograms. Which statements are true? Select all that apply.

1) Uranus weighs about 1.5 × 10¹ times as much as earth.
2) Mercury weighs about 1.5 × 10⁻⁷ times as much as the sun.
3) Mercury weighs about 5 × 10⁻¹ times as much as earth.
4) Earth weighs about 2 × 10¹ times as much as mercury.

Answer 1

The correct statements are that Mercury weighs about 1.5 × 10⁻⁷ times as much as the Sun and Earth weighs about 2 × 10¹ times as much as Mercury; the other statements are false.

Step-by-step explanation:

Comparing the masses of the Sun, Mercury, Earth, and Uranus involves applying principles of ratio and proportion. Let us evaluate the given statements one by one:

1. Uranus weighs about 1.5 × 10¹ times as much as Earth. This statement is false because Uranus's mass (9 × 10²⁵ kg) divided by Earth's mass (about 6 × 10²⁴ kg) equals approximately 1.5 × 10¹, which is not the correct ratio.
2. Mercury weighs about 1.5 × 10⁻⁷ times as much as the Sun. This statement is true. Dividing Mercury's mass (3 × 10²³ kg) by the Sun's mass (2 × 10³⁰ kg) yields 1.5 × 10⁻⁷ as the ratio.
3. Mercury weighs about 5 × 10⁻¹ times as much as Earth. This statement is false; the actual ratio is closer to 1/18th or approximately 5.5 × 10⁻².
4. Earth weighs about 2 × 10¹ times as much as Mercury. This statement is true. Earth's mass (6 × 10²⁴ kg) divided by Mercury's mass (3 × 10²³ kg) equals 2 × 10¹.