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A light year is the distance that light can travel in one year. 1 light year = 9,460,000,000,000 km. The average distance between Earth and Sun is 1.496 × 10⁸ km. Is the distance between Earth and the Sun greater than, less than or equal to one light year

Solution:

Given, a light year is the distance that light can travel in one year.

1 light year = 9,460,000,000,000 km

Average distance between Earth and Sun is 1.496 × 10⁸ km.

We have to determine if the distance between Earth and the Sun greater than, less than or equal to one light year.

1 light year = 9,460,000,000,000 km

= 946 × 10¹⁰

= 9.46 × 10² × 10¹⁰

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m × aⁿ = a^m+n

= 9.46 × 10^{2 + 10}

= 9.46 × 10¹² km -------------------------- (1)

Average distance between Earth and Sun = 1.496/10000 × 10⁸ × 10⁴

= 1.496/10000 × 10⁴ × 10⁸

= 1.496/10000 × 10^{4 + 8}

= 1.496/10000 × 10¹²

= 0.0001496 × 10¹² km ----------------- (2)

From (1) and (2),

0.0001496 × 10¹² < 9.46 × 10¹²

Therefore, the distance between Earth and the Sun is less than one light year.

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☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 91 (b)

Summary:

A light year is the distance that light can travel in one year. 1 light year = 9,460,000,000,000 km.

The average distance between Earth and Sun is 1.496 × 10⁸ km. The distance between Earth and the Sun is less than one light year.

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