Problem 122 - College Algebra Essentials

Question

Convert 365 days (one year) to hours, to minutes, and, finally, to seconds, to determine how many seconds there are in a year. Express the answer in scientific notation.

Step-by-Step Solution

Answer

The total number of seconds in one year, expressed in scientific notation, is \(3.1536 \times 10^7\) seconds.

Step 1: Convert Days to Hours

Start with the number of days in one year, which is 365 days. To convert this to hours, use the conversion factor \(1 day = 24 hours\). Multiply 365 days with 24 to get the total hours in a year.

Step 2: Convert Hours to Minutes

With the total hours in a year calculated, now convert this into minutes. Use the conversion factor \(1 hour = 60 minutes\). Multiply the result from Step 1 by 60 to get the total minutes in a year.

Step 3: Convert Minutes to Seconds

Next, convert the total minutes in a year to seconds using the conversion factor \(1 minute = 60 seconds\). Multiply the result from Step 2 by 60 to obtain the total seconds in a year.

Step 4: Convert to Scientific Notation

Having calculated the total number of seconds in a year, the final step is to express this number in scientific notation. Remember that scientific notation has this form: \(a \times 10^n\), where \(1 \leq |a| < 10\) and \(n\) is an integer. Divide the total seconds by a power of ten to get the number \(a\) and the exponent \(n\).