Problem 9 - Chemistry: The Central Science

Question

When you convert units, how do you decide which part of the conversion factor is in the numerator and which is in the denominator? [Section 1.6]

Step-by-Step Solution

Answer

To decide which part of the conversion factor is in the numerator and which is in the denominator when converting units, first identify the given unit and the desired unit. Then, find the appropriate conversion factor relating the two units. Set up the conversion factor as a fraction, placing the desired unit in the numerator and the given unit in the denominator. This ensures that the given unit cancels out, leaving the desired unit when multiplied with the given value. Finally, simplify the result if necessary.

Step 1: Identify the given unit and desired unit

First, it is important to determine which unit is given in the problem and which unit we want to convert it to. This will help us decide how to set up the conversion factor correctly.

Step 2: Determine the conversion factor required

Once the given unit and desired unit are identified, find the appropriate conversion factor that relates the two units. Conversion factors can be found in reference books, conversion tables, or online resources. Remember that the conversion factor is a ratio that expresses the relationship between two units.

Step 3: Set up the conversion factor correctly

Write the conversion factor as a fraction such that the numerator contains the desired unit and the denominator contains the given unit. Setting up the conversion factor in this manner ensures that the given unit will cancel out, and the desired unit will remain in the calculation.

Step 4: Multiply the given value with the conversion factor

Now that the conversion factor is correctly set up, multiply the given value with this conversion factor. When multiplying, the given unit in the denominator will cancel out with the given unit in the value you want to convert, leaving only the desired unit in the result.

Step 5: Simplify the result

After performing the multiplication, simplify the result, if necessary. This will provide the final value with the desired unit. To summarize, when you convert units using a conversion factor, the key is to identify the given and desired units, determine the appropriate conversion factor, set up the conversion factor such that the given unit cancels out and the desired unit remains, multiply the given value with the conversion factor, and simplify the result if necessary.