Problem 43 - Chemistry Matter and Change

Question

Perform the following calculations. Round the answers. a. 4.84 \(\mathrm{m} \div 2.4 \mathrm{s} \quad\) b. 60.2 \(\mathrm{m} \div 20.1 \mathrm{s}\) \(\quad\) c. 102.4 \(\mathrm{m} \div 51.2 \mathrm{s} \quad\) d. 168 \(\mathrm{m} \div 58 \mathrm{s}\)

Step-by-Step Solution

Answer

a. 2.0 m/s, b. 3.0 m/s, c. 2.0 m/s, d. 2.9 m/s

Step 1: Calculate 4.84 m ÷ 2.4 s

To divide 4.84 meters by 2.4 seconds, perform the division: \( \frac{4.84}{2.4} = 2.0166667 \). Round this result to one decimal place, which gives us 2.0 m/s.

Step 2: Calculate 60.2 m ÷ 20.1 s

Divide 60.2 meters by 20.1 seconds: \( \frac{60.2}{20.1} = 2.9950248756 \). Round this to one decimal place, resulting in 3.0 m/s.

Step 3: Calculate 102.4 m ÷ 51.2 s

Perform the division: \( \frac{102.4}{51.2} = 2.0 \). This value is already to one decimal place at 2.0 m/s.

Step 4: Calculate 168 m ÷ 58 s

Divide 168 meters by 58 seconds: \( \frac{168}{58} = 2.896551724 \). Round this number to one decimal place to get 2.9 m/s.

Key Concepts

Understanding Division Problems

Division is the process of splitting a number into equal parts and determining how many times one number is contained in another. In the exercise, each problem involves dividing a distance measured in meters (m) by a time measured in seconds (s). This provides the speed, which tells us how fast something is moving.
To tackle these division problems:

• Identify the dividend (the number to be divided) and the divisor (the number you divide by).
• Perform the division: Set up the problem as a fraction.
• Solve the division using a calculator or long division.

By solving these problems, students practice how to operate with numbers practically, a key skill in both mathematics and real-world applications.

Mastering Rounding Decimals

Rounding decimals is an essential skill when final results need to be expressed in simpler terms. In this exercise, each calculation result was rounded to one decimal place. Rounding means finding the closest approximation of a number.
To round to a single decimal place:

• Identify the number in the second decimal place.
• If this number is 5 or higher, round the first decimal place up by one. If it's lower, keep the first decimal place the same.
• Apply this rule to each final result of your division problems.

Rounding helps streamline numbers, making them easier to read and understand while maintaining a reasonable degree of accuracy.

Insights into Speed Calculation

Speed is a measure of the distance covered per unit of time. The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] In the exercise, each division problem calculates speed by dividing the total distance by the time taken. This leads to the results expressed as meters per second (m/s).

• A higher quotient indicates a higher speed.
• Understanding speed is crucial for interpreting how fast an object is traveling.
• This understanding is applicable across various scenarios, from calculating travel time to analyzing sports performance.

Learning how to calculate speed enhances comprehension of motion and aids students in practical assessments of dynamic situations.

Breaking Down Mathematical Steps

Each mathematical problem consists of a series of steps that guide towards the solution. By closely examining these steps, students learn to apply structured thinking to tackle diverse problems.
For dividing numbers as shown in the exercise:

• First, write down the division operation.
• Use consistent methods to solve, such as calculators or long-hand division.
• Verify the precision of your results before rounding.
• Round the resulting quotient correctly to the specified decimal places.

Learning to follow a consistent process is pivotal for solving complex problems efficiently. Emphasizing these steps builds confidence in students, equipping them with strategies for future mathematical challenges.