Math Problem Statement

The distance from Earth to the moon is 2.4 × 10^5 miles. The distance from Earth to the sun is 9.3 × 10^7 miles. Complete the sentence: The distance from Earth to the sun is _______ × 10 _______ miles greater than the distance from Earth to the moon.

Solution

The image asks to compare the distance from Earth to the Moon and the distance from Earth to the Sun.

The given data is:

  • Distance from Earth to the Moon: 2.4×1052.4 \times 10^5 miles
  • Distance from Earth to the Sun: 9.3×1079.3 \times 10^7 miles

The task is to complete the sentence: "The distance from Earth to the Sun is ?×10?\boxed{\text{?}} \times 10^{\boxed{\text{?}}} miles greater than the distance from Earth to the Moon."

Steps to solve:

  1. Divide the distance from Earth to the Sun by the distance from Earth to the Moon. 9.3×1072.4×105\frac{9.3 \times 10^7}{2.4 \times 10^5}

  2. Simplify the expression: 9.32.4×1075=3.875×102\frac{9.3}{2.4} \times 10^{7-5} = 3.875 \times 10^2

So, the distance from Earth to the Sun is approximately 3.875×1023.875 \times 10^2 times greater than the distance from Earth to the Moon.

Thus, the first blank should be 3.875 and the second blank should be 2.

Would you like a detailed breakdown of the calculations or have any questions?

Related Questions:

  1. What is the approximate distance in miles from Earth to the Sun?
  2. How many times farther is the Sun from Earth compared to the Moon?
  3. How would this comparison change using kilometers instead of miles?
  4. What is the significance of scientific notation in measuring large distances?
  5. How can we estimate distances to celestial bodies using this method?

Tip: Scientific notation is essential when dealing with very large or very small numbers, making calculations more manageable and reducing errors.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Division
Exponent Rules

Formulas

(Distance to Sun) ÷ (Distance to Moon)
10^7 ÷ 10^5 = 10^(7-5)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 6-8