Question

A penny has a mass of 2.50 g, and the moon has a mass of 7.25 × 10²² kg. What is the ratio of the mass of the moon to the mass of the penny?

A) 2.9×10²²
B) 2.9×10⁻¹⁹
C) 2.9×10⁻²⁰
D) 2.9×10¹⁹
E) 2.9×10²⁰

Answer 1

To find the ratio of the moon's mass to the penny's mass, convert the penny's mass to kilograms and divide by the moon's mass. The correct ratio, expressed in scientific notation, is 2.9× 10¹¹, option D.

Step-by-step explanation:

To find the ratio of the mass of the moon to the mass of a penny, we divide the mass of the moon by the mass of the penny and express it in scientific notation, if necessary. Given that:

• Moon's mass = 7.25 × 10²² kg
• Penny's mass = 2.50 g

First, we need to convert the mass of the penny to kilograms to match the units of the moon's mass:

2.50 g × (1 kg / 1000 g) = 0.0025 kg

Now, we calculate the ratio:

Ratio = Moon's mass / Penny's mass

Ratio = (7.25 × 10²² kg) / 0.0025 kg

Ratio = 2.9× 10²² / 0.0025

Ratio = 2.9× 10²² / 2.5 × 10⁻³

Ratio = 2.9× 10¹¹µ

To express it in scientific notation, we add the exponents:

Ratio = 2.9× 10¹¹ (10¹¹ = 10²² - 10⁻³)

Thus, the correct answer is 2.9× 10¹¹, which is represented by option D.