Question

One light year is equal to 9.467×10 to the power 15m and 1 AU is 1.496 × 10 to the power 11 m . Find the order of magnitude of light year in terms of AU.

Answer 1

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Answer 2

The order of magnitude is 5.

Given - Value of light year and AU

Find - Order of magnitude of light year in terms of AU.

Solution - Order of magnitude refers to the power of 10, when the number is written in scientific notation. We are given the value of one light and years and one AU. We will be relating the two to find the order of magnitude.

So, 1.496×10¹¹ meters = 1 AU

1 meter = $\frac{1}{1.496 \times {10}^{11} }$

AU

Now, 1 light year will be equal to AU -

9.467×10¹⁵ meters = $\frac{9.467 \times {10}^{15} }{1.496 \times {10}^{11} }$

So, the value of one light year in AU is = 63,282.1 AU

Rewriting the number in scientific notation -

Value of one light year in AU = 0.63×10⁵

Therefore, as per the given calculation, the order of magnitude of light year in terms of AU is 5.

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