Problem 8 - Prealgebra

Question

A use the tables of conversion factors given in this section and other sections in this chapter to make the following conversions. (Round your answers to the nearest hundredth.) [Example 1] 4 minutes 40 seconds to a. Seconds b. Minutes

Step-by-Step Solution

Answer

4 minutes 40 seconds is 280 seconds and 4.67 minutes.

Step 1: Convert Minutes to Seconds

First, let's convert the 4 minutes into seconds. We know that 1 minute is 60 seconds. So, multiply 4 minutes by 60: \[4 \text{ minutes} \times 60 \text{ seconds/minute} = 240 \text{ seconds}\]

Step 2: Add Remaining Seconds

Add the given 40 seconds to the total number of seconds we found:\[240 \text{ seconds} + 40 \text{ seconds} = 280 \text{ seconds}\]So, 4 minutes 40 seconds is 280 seconds.

Step 3: Convert Seconds Back to Minutes

Now, convert 280 seconds back to minutes. Since 1 minute is 60 seconds, divide the total number of seconds by 60:\[280 \text{ seconds} \div 60 \text{ seconds/minute} = 4.6667 \text{ minutes}\]Round 4.6667 to the nearest hundredth: 4.67 minutes.

Key Concepts

Seconds Conversion

To convert time from minutes to seconds, knowing the basic conversion factor is key. One minute equals 60 seconds. When you are faced with a problem asking to convert minutes into seconds, simply multiply the number of minutes by 60. This multiplication allows you to transform the minutes into their equivalent second value.

For example, if you have 4 minutes, multiplying it by 60 seconds per minute yields:

• 4 minutes × 60 seconds/minute = 240 seconds

After converting the minutes, remember to add any extra seconds given in the problem to your total. In our example, you would add 40 seconds to the 240 seconds already calculated:

• 240 seconds + 40 seconds = 280 seconds

In conclusion, following these two steps helps you calculate the full duration in seconds smoothly.

Minutes Conversion

Converting seconds back to minutes requires dividing the total seconds by 60, since one minute is made up of 60 seconds. This step reverses the initial conversion and gives you the time in minutes, including any fractional minutes.

Take our example of 280 seconds. To find out how many minutes that is, divide by 60:

• 280 seconds ÷ 60 seconds/minute = 4.6667 minutes

When you perform this division, you’ll often get a decimal number, which represents minutes with tenths, hundredths, and so on of a minute. It shows both the full minute and any leftover seconds as fractions of a minute. This approach ensures a comprehensive understanding of time dealings in both units.

Rounding Numbers

Rounding is a crucial step to make numbers easier to work with and understand, especially when dealing with decimals.

After converting total seconds into minutes in your calculations, you may not want to leave the answer as a long decimal. You can refine it by rounding, often to the nearest hundredth to maintain precision while still simplifying the result.

In our example:

• 4.6667 rounds to 4.67 when rounded to the nearest hundredth

To round, observe the third decimal place. If it's 5 or greater, round the second decimal place up by one. If less, keep the number the same. This smoothing out of the decimal ensures the representation of the time is not only accurate but also clearer to communicate and comprehend.