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What is the standard form of 2 years in seconds?

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6.3072 × 105 seconds

6.3072 × 107 seconds

63072 × 105 seconds

63072 × 107 seconds

answer is B.

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Detailed Solution

We are given 2 years.
We know that,

1 year = 365days

⇒ 2 year = 2×365 days

⇒ 2 year = 730 days

∵ 1day = 24 hour

⇒ 730 days = 17520 hours

∵ 1 hour = 60 min

⇒ 17520 hour = 17520 ×60 min

⇒ 17520 hour = 1051200 min

∵ 1 min = 60 seconds

⇒ 1051200 min = 1051200×60 sec

⇒ 1051200 min = 63072000 sec

⇒ 2 years = 63072000 sec

Write the standard form.
Therefore we have,

63072000 = 63072 × 103

⇒ 63072000 = 63072 × 1000010000 × 103

⇒ 63072000 = 6.3072 × 104 × 103

Apply the law of exponent

a m × a n = a m + n .

⇒ 63072000 = 6.3072 × 107

Therefore, the standard form of 2 years is

6.3072 × 107 seconds .

Hence option (2) is correct.

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