Question

Consider the following information.

1 hour = 3.6 · 103 seconds
1 day = 24 hours
1 year = 3.65 · 102 days

Use scientific notation to calculate the number of hours in one year. In your final answer, include all of your calculations.

Answer 1

Answer:
`1\text{ year}=8.76*10^3\text{ hours}`

Explanation:

Given:
`\text{1 hour}=3.6*10^3\text{ seconds}`

`\\1\text{ day=24 hours}...................(1)\\\text{1 year = }3.65*10^\text{ days}`

`\\\Rightarrow\ 1\text{ year}=3.65*10^2*24\text{ hours}...........(\text{ from (1)})\\\Rightarrow\ 1\text{ year}=3.65*24*10^2\text{ hours}\\\Rightarrow\ 1\text{ year}=87.6*10^2\text{ hours}\\\Rightarrow\ 1\text{ year}=8.76*10^3\text{ hours}................\text{In scientific notation}`

Hence,
`1\text{ year}=8.76*10^3\text{ hours}`

Answer 2

1 hour = 3.6 x 10^3 seconds
1 day = 24 hours
1 year = 3.65 x 10^2 days

By process of dimensional analysis:
1 yr x 3.65x10^2 days/1 yr x 24hrs/1day = 8,760 hours

In scientific notation: 8.760 x 10^3 hours