What is the equation that shows the factor labels to convert 75 grams to ounces?
a. 75 g × 0.03527 oz/g
b. 75 g ÷ 0.03527 oz/g
c. 75 g × 0.0022 oz/g
d. 75 g ÷ 0.0022 oz/g
The Correct Answer and Explanation is:
The correct answer is a. 75 g × 0.03527 oz/g.
Explanation:
To convert grams (g) to ounces (oz), you need a conversion factor that relates the two units. The conversion factor for grams to ounces is approximately 0.03527 ounces per gram (oz/g). This factor indicates that for every gram, there are 0.03527 ounces.
The equation you need to use for the conversion is:
[
75 \, \text{grams} \times \frac{0.03527 \, \text{oz}}{\text{g}} = 75 \times 0.03527 \, \text{oz}
]
Step-by-step Breakdown:
- Identify the conversion factor:
You need to know how many ounces are in one gram. From the metric system, the conversion factor is:
[
1 \, \text{gram} = 0.03527 \, \text{ounces}.
] - Set up the conversion equation:
To convert grams into ounces, multiply the number of grams (75 g) by the conversion factor (0.03527 oz/g):
[
75 \, \text{g} \times \frac{0.03527 \, \text{oz}}{\text{g}} = 75 \times 0.03527 \, \text{oz} = 2.64525 \, \text{oz}.
] - Result:
When you multiply 75 grams by 0.03527 oz/g, you get approximately 2.645 ounces.
Why the Other Options Are Incorrect:
- Option b (75 g ÷ 0.03527 oz/g):
Dividing by the conversion factor would be incorrect because you are trying to convert grams to ounces. You should multiply, not divide. - Option c (75 g × 0.0022 oz/g):
This factor is incorrect. It seems to be a conversion factor for pounds to grams (since 1 pound is approximately 453.6 grams, and 1 ounce is 1/16 of a pound, but the factor 0.0022 oz/g is not used for grams to ounces conversion). - Option d (75 g ÷ 0.0022 oz/g):
Again, dividing by the conversion factor is incorrect for the same reason as option b, and the factor is not suitable for grams to ounces.
In conclusion, to convert grams to ounces, multiply by the correct conversion factor 0.03527 oz/g. Thus, option a is the correct equation to use.