This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to the problem: Q20. Real-Life connect: Find the approximate distance from Earth to at least 3 planets in km. Express each in standard form and compare using power of 10. Step 1: Identify three planets and their approximate average distances from Earth. We will use Mars, Jupiter, and Saturn. • Approximate average distance from Earth to Mars: 225,000,000 km • Approximate average distance from Earth to Jupiter: 778,000,000 km • Approximate average distance from Earth to Saturn: 1,400,000,000 km Step 2: Express each distance in standard form (scientific notation). Standard form is written as a × 10^n, where 1 a < 10 and n is an integer. • Mars: 225,000,000 km = 2.25 × 10^8 km • Jupiter: 778,000,000 km = 7.78 × 10^8 km • Saturn: 1,400,000,000 km = 1.4 × 10^9 km Step 3: Compare the distances using powers of 10. To compare, we first look at the exponent of 10. A larger exponent means a larger number. • Saturn's distance has an exponent of 9 (10^9). • Mars' and Jupiter's distances both have an exponent of 8 (10^8). Since 10^8 < 10^9, Saturn is farther than both Mars and Jupiter. To compare Mars and Jupiter, we look at their coefficients because their powers of 10 are the same: 2.25 < 7.78. So, Mars is closer than Jupiter. Step 4: State the comparison in ascending order. The distances in ascending order are: Mars (2.25 × 10^8 km) < Jupiter (7.78 × 10^8 km) < Saturn (1.4 × 10^9 km). The approximate distances from Earth to three planets, expressed in standard form and compared, are: • Mars: 2.25 × 10^8 km • Jupiter: 7.78 × 10^8 km • Saturn: 1.4 × 10^9 km Comparison: Mars < Jupiter < Saturn. What's next? Send 'em!