Question

Math / Science help

Answer in scientific notation

Answer 1

7.60×10⁶ s

Explanation:

You want the number of seconds in 0.24084 Earth years.

Timekeeping

An Earth day is defined as 24 hours of 3600 seconds each. On average, there are 365.2425 days in a year, so an Earth year will be ...

(365.2425 da)(24 h/da)(3600 s/h) . . . . seconds

Then 0.24084 Earth years will be ...

(365.2425 da/yr)(24 h/da)(3600 s/h)(0.24084 yr) ≈ 7.60×10⁶ s

The period of an orbit of Mercury is about 7.60×10⁶ seconds.

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Additional comment

The Gregorian calendar has 146097 days in 400 years. That is about 2 hours 58 minutes 34 seconds too long over that period. Here, we ignore this unadjusted error in our current calendar.

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Answer 2

`\sf T_(Mercury) = 7.59* 10^6 seconds`

Explanation:

We have

1 Earth year = 365 days

0.24084 Earth years = 0.24084 × 365 days

= 87.9066 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

87.9066 days no 24 hours/day × 60 minutes/hour × 60 seconds/minute = 7595130.24 seconds

Rounding the coefficient to the nearest hundredth, we get:

`\sf T_(Mercury) = 7.59 * 10^6 seconds`

Therefore, the answer in scientific notation is:

`\sf T_(Mercury) = 7.59 * 10^6 seconds`