Problem 7 - 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] 5 minutes 20 seconds to a. Seconds b. Minutes

Step-by-Step Solution

Answer

a. 320 seconds b. 5.33 minutes

Step 1: Convert Minutes to Seconds

First, convert the minutes into seconds. We know that 1 minute is equal to 60 seconds. Since we have 5 minutes, we multiply 5 by 60 to get the total number of seconds from the minutes. \[ 5 \text{ minutes} = 5 \times 60 \text{ seconds} = 300 \text{ seconds} \]

Step 2: Add Additional Seconds

Now that we have converted the minutes into seconds, we need to include the additional seconds given in the problem. We add 20 seconds to the 300 seconds we have already calculated.\[ 300 \text{ seconds} + 20 \text{ seconds} = 320 \text{ seconds} \]

Step 3: Convert Seconds to Decimal Minutes

To find out how many minutes 320 seconds equals, divide the total number of seconds by 60 since there are 60 seconds in a minute.\[ \frac{320 \text{ seconds}}{60} = 5.3333 \text{ minutes} \]

Step 4: Round Minutes to the Nearest Hundredth

Round the result of 5.3333 minutes to the nearest hundredth. This involves looking at the third decimal place, which is 3, and determining the rounded value. Rounded to the nearest hundredth, 5.3333 minutes becomes 5.33 minutes.

Key Concepts

Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another. It is an essential skill in everyday math and science.

When we perform unit conversions, we maintain the value but express it in a different way. For example, in our exercise, we convert time from minutes and seconds into seconds, and then into minutes to understand duration better.

To convert from one unit to another, we use a conversion factor, which is a number used to change one unit of measure into another. In the case of time, we use the relation that 1 minute equals 60 seconds.

Here's how to do it:

• Identify the units you're converting from and to.
• Find the conversion factor. For example, if converting minutes to seconds, use 1 minute = 60 seconds.
• Multiply or divide by this factor to get the number in the new unit.

Unit conversion allows us to compare and compute accurately, especially when dealing with different systems or formats.

Rounding Numbers

Rounding numbers is a technique used to simplify a number while keeping its value similar to the original number. It is essential for making calculations easier or when a precise value is not necessary.

In our exercise, we had to round 5.3333 minutes to the nearest hundredth. Rounding to the nearest hundredth means we keep two decimal places.

To round a number, look at the digit in the place you wish to round to and the digit immediately afterward. In this exercise:

• Identify the hundredth place (which is 3 in 5.3333).
• Check the digit right next to it. If it is 5 or more, increase the hundredth place by 1.
• If it is less than 5, leave the hundredth place as it is.

Following this, 5.3333 rounds down to 5.33 because the third digit is 3, which is less than 5.

Rounding helps make complex numbers simpler and is often used in practical contexts where an exact number is unnecessary, ensuring easier comparisons and estimates.

Prealgebra

Prealgebra is a branch of mathematics that prepares students for algebra by covering fundamental concepts and operations. It acts as the building block for understanding more complex math.

The exercise incorporates several key prealgebra skills such as unit conversion and rounding, which are fundamental concepts. These skills are crucial to grasp because they form the basis for more advanced problem-solving.

Key aspects of prealgebra include:

• Understanding numbers and operations, including integers, fractions, and decimals.
• Handling concepts like unit conversions and approximations.
• Learning how to manipulate mathematical expressions and equations.

Mastery of prealgebra ensures a smoother transition into algebra, where operations become more complex, and abstract thinking becomes necessary. Understanding these basic functions aids in solving equations efficiently and prepares students for higher-level math topics.