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Real-Line 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.

Mathematics

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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.

  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
  2. Express each distance in standard form (scientific notation).

    Standard form is written as a×10na \times 10^n, where 1≤a<101 \le a < 10 and nn is an integer.

    • Mars: 225,000,000 km=2.25×108 km225,000,000 \text{ km} = 2.25 \times 10^8 \text{ km}
    • Jupiter: 778,000,000 km=7.78×108 km778,000,000 \text{ km} = 7.78 \times 10^8 \text{ km}
    • Saturn: 1,400,000,000 km=1.4×109 km1,400,000,000 \text{ km} = 1.4 \times 10^9 \text{ km}
  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 (10910^9).
    • Mars' and Jupiter's distances both have an exponent of 8 (10810^8).

    Since 108<10910^8 < 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<7.782.25 < 7.78.
    So, Mars is closer than Jupiter.

  4. State the comparison in ascending order.

    The distances in ascending order are:
    Mars (2.25×108 km2.25 \times 10^8 \text{ km}) < Jupiter (7.78×108 km7.78 \times 10^8 \text{ km}) < Saturn (1.4×109 km1.4 \times 10^9 \text{ km}).

    The approximate distances from Earth to three planets, expressed in standard form and compared, are:

    • Mars: 2.25×108 km\boxed{2.25 \times 10^8 \text{ km}}
    • Jupiter: 7.78×108 km\boxed{7.78 \times 10^8 \text{ km}}
    • Saturn: 1.4×109 km\boxed{1.4 \times 10^9 \text{ km}} Comparison: Mars<Jupiter<Saturn\boxed{\text{Mars} < \text{Jupiter} < \text{Saturn}}.
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