Question

Estimate the number of seconds in a year. Show your reasoning using scientific notation.

1 year ≈ 365 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

(1 point)
Responses

3.2×108
3 point 2 times 10 to the 8th power

3.6×105
3 point 6 times 10 to the 5th power

3.6×106
3 point 6 times 10 to the 6th power

3.2×107

Answer 1

To estimate the number of seconds in a year, we can start with the conversions provided:

1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

Now, let's calculate the total number of seconds in one year:

1. **Calculate seconds in a day**:
\[
\text{Seconds in a day} = 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute}
\]
\[
= 24 \times 60 \times 60
\]
\[
= 24 \times 3600 = 86400 \text{ seconds/day}
\]

2. **Calculate seconds in a year**:
\[
\text{Seconds in a year} = 365 \text{ days/year} \times 86400 \text{ seconds/day}
\]
\[
= 365 \times 86400
\]
Now, let's break this down using scientific notation:
\[
365 \approx 3.65 \times 10^2
\]
\[
86400 = 8.64 \times 10^4
\]

Now multiply these two results:
\[
(3.65 \times 10^2) \times (8.64 \times 10^4) = (3.65 \times 8.64) \times (10^2 \times 10^4)
\]

Calculate \( 3.65 \times 8.64 \):
\[
3.65 \times 8.64 \approx 31.56
\]

Now adding the powers of 10:
\[
10^2 \times 10^4 = 10^{(2 + 4)} = 10^6
\]
Thus:
\[
\text{Seconds in a year} \approx 31.56 \times 10^6
\]

We can convert this to proper scientific notation:
\[
31.56 \times 10^6 \approx 3.156 \times 10^7
\]

Rounding \(3.156\) gives us approximately \(3.2\). Therefore, the estimated number of seconds in a year can be expressed in scientific notation as:
\[
\boxed{3.2 \times 10^7}
\]

The correct response is:
**3.2×10^7**.