Use the following information to complete parts I, II, and III.

Question

Use the following information to complete parts I, II, and III.
1 hour= 3,600 seconds

1 year= 31,556,952 seconds

Part I: Use scientific notation to estimate the number of hours in one year.

Part II: Use scientific notation to calculate the exact number of hours in one year.

Part III: In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences in your answers.

GPT-4o mini · Answer

### Part I: Estimate the Number of Hours in One Year To estimate the number of hours in one year using scientific notation, we know there are 24 hours in a day and approximately 365 days in a year. Therefore, we can calculate: $$ \text{Estimated hours in one year} = 24 \, \text{hours/day} \times 365 \, \text{days/year} \approx 8,760 \, \text{hours/year} $$ In scientific notation, this can be expressed as: $$ 8,760 \approx 8.76 \times 10^3 \, \text{hours} $$ ### Part II: Calculate the Exact Number of Hours in One Year To calculate the exact number of hours in one year, we will use the exact value of seconds provided (1 year = 31,556,952 seconds) and the conversion of seconds to hours (1 hour = 3,600 seconds): $$ \text{Exact hours in one year} = \frac{31,556,952 \, \text{seconds/year}}{3,600 \, \text{seconds/hour}} \approx 8,760.82 \, \text{hours/year} $$ In scientific notation, this can be expressed as: $$ 8,760.82 \approx 8.76 \times 10^3 \, \text{hours} $$ ### Part III: Comparison of Answers The results from parts I and II are quite similar; both estimates yield a value of approximately $ 8.76 \times 10^3 $ hours per year. However, part I provides a rough estimate, rounding to $ 8,760 $ hours, while part II offers a more precise calculation, yielding $ 8,760.82 $ hours. This slight difference highlights that while the estimation is close and useful for quick calculations, the exact calculation accounts for the additional fraction of an hour, which can be significant in contexts requiring accuracy.

Answer

can you make it a little less advanced

GPT-4o mini · Answer

Sure! Here’s a simpler version: ### Part I: Estimate the Number of Hours in One Year To estimate the number of hours in one year, we know there are 24 hours in a day and around 365 days in a year. So, we can calculate: $$ \text{Estimated hours in one year} = 24 \, \text{hours/day} \times 365 \, \text{days/year} \approx 8,760 \, \text{hours/year} $$ In scientific notation, this is: $$ 8,760 \approx 8.76 \times 10^3 \, \text{hours} $$ ### Part II: Calculate the Exact Number of Hours in One Year Now let's calculate the exact number of hours in one year using the provided data (1 year = 31,556,952 seconds) and knowing that there are 3,600 seconds in an hour: $$ \text{Exact hours in one year} = \frac{31,556,952 \, \text{seconds/year}}{3,600 \, \text{seconds/hour}} \approx 8,760.82 \, \text{hours/year} $$ In scientific notation, this is: $$ 8,760.82 \approx 8.76 \times 10^3 \, \text{hours} $$ ### Part III: Comparison of Answers The answers from parts I and II are very similar. Both give about $ 8.76 \times 10^3 $ hours in a year. Part I is an estimate and uses the rounded number 8,760 hours, while part II gives a more exact number of 8,760.82 hours. The small difference shows that while the estimate is close enough for many uses, the exact calculation is more accurate.

Answer

can you do it without all the symbols and slashes

GPT-4o mini · Answer

Of course! Here’s a version without the symbols and slashes:

Part I: Estimate the Number of Hours in One Year

To estimate the number of hours in one year, we know there are 24 hours in a day and about 365 days in a year. So, we can calculate:

Estimated hours in one year equals 24 hours per day times 365 days per year, which is approximately 8,760 hours in a year.

In simpler terms, we can write this in scientific notation as 8.76 times ten to the power of 3 hours.

Part II: Calculate the Exact Number of Hours in One Year

Now, let's find the exact number of hours in one year using the information given. One year equals 31,556,952 seconds, and there are 3,600 seconds in an hour. Therefore:

The exact number of hours in one year equals 31,556,952 seconds divided by 3,600 seconds per hour, which gives us approximately 8,760.82 hours in a year.

In scientific notation, this is also written as 8.76 times ten to the power of 3 hours.

Part III: Comparison of Answers

The results from parts I and II are very similar. Both calculations give around 8.76 times ten to the power of 3 hours in a year. Part I provides a rough estimate of 8,760 hours, while part II offers a more precise total of 8,760.82 hours. The small difference between the two shows that the estimate is close enough for many uses, but the exact calculation gives a bit more detail.