Problem 37 - Prealgebra

Question

Set up the following problems as we have set up the examples in this section. Then use a calculator for the calculations and round your answers to the nearest hundredth. \(500 \mathrm{g}\) to ounces

Step-by-Step Solution

Answer

500 grams is approximately 17.64 ounces.

Step 1: Understand the Conversion Factor

To convert grams to ounces, we need to know the conversion factor. The conversion factor from grams to ounces is 1 ounce = 28.3495 grams. We will use this factor to convert 500 grams to ounces by dividing 500 by 28.3495.

Step 2: Set Up the Equation

To set up the conversion equation, apply the conversion factor:\[ \text{Ounces} = \frac{500 \, \text{grams}}{28.3495 \, \text{grams/ounce}} \]This equation allows us to convert the measurement from grams to ounces.

Step 3: Perform the Calculation

We will use a calculator to perform the division:\[ \text{Ounces} = \frac{500}{28.3495} \approx 17.63698 \]Step 4: Round the Result to the Nearest HundredthNow, round 17.63698 to the nearest hundredth, which gives us approximately 17.64 ounces.

Step 4: Round the Result to the Nearest Hundredth

We need to round the result of 17.63698 to the nearest hundredth: The digit in the hundredth place is 3, and the digit to the right is 6. Since 6 is greater than 5, we round up, changing the 3 to a 4. Thus, the final rounded result is 17.64 ounces.

Key Concepts

Unit Conversion

Unit conversion is a crucial skill that helps transform one unit of measurement into another, making it easier to compare quantities measured in different units. When converting units, you use what's called a "conversion factor." A conversion factor is a ratio that expresses how many of one unit are equal to another unit. For example, to convert grams to ounces, we use the conversion factor: 1 ounce is equal to 28.3495 grams.

• Identify the units you want to convert from and to. In our example, from grams to ounces.
• Find the appropriate conversion factor. Here, it's 1 ounce = 28.3495 grams.
• Use the conversion factor to set up your equation and solve. Divide the number of grams by the grams per ounce: \(\frac{500 \, \text{grams}}{28.3495 \, \text{grams/ounce}}\).

This gives you the equivalent measurement in the new unit. Understanding conversion factors and how to apply them ensures accurate calculations and comparisons across different measurement systems.

Rounding Numbers

Rounding numbers is used to simplify figures, especially when they have many decimal places, into something more digestible. This process helps in improving the readability and usability of numbers, especially in everyday applications. For example, in our conversion problem, we rounded 17.63698 to 17.64.

• Identify the place to which you want to round. Common places include tens, hundreds, tenths, or hundredths.
• When rounding to the hundredth place, look at the number in the thousandth place. If it's 5 or more, increase the hundredth's digit by 1; if less, leave it as is.
• For 17.63698, the hundredth digit was 3, and the digit to the right was 6. Since 6 is more than 5, we rounded up to get 17.64.

Rounding not only helps in making numbers simpler but also allows for clearer communication of data, which can be especially useful in scientific and financial calculations.

Using Conversion Factors

Conversion factors are the bridge between differing measurement systems, enabling the transition from one unit of measurement to another seamlessly. When working with conversion factors, it's important to follow a systematic approach to avoid errors. Here's how you can effectively use conversion factors:

• Write down the conversion factor clearly. A conversion factor is essentially a fraction that equals 1, such as \(\frac{1 \, \text{ounce}}{28.3495 \, \text{grams}}\).
• Set up the conversion equation based on the units involved. Ensure that the unit you want to cancel out is set opposite in the fraction.
• Ensure the units cancel out correctly, leaving you with the desired unit at the end.

For our example, the conversion factor allowed us to convert 500 grams into ounces, ending with 17.63698 ounces before rounding. Mastery of using conversion factors is vital for any science or math-related tasks, as well as for real-world applications like cooking or traveling.