The density of a certain material is such that it weighs 9600 milligrams per fluid ounce of volume. Express this density in kilograms per cup.
9600mg/1oz * 1kg/(10^6 mg) * 8oz/cup = (9600*8)/10^6 kg/cup
= 0.0768 kg/cup
Well, that's quite the interesting conversion request! Let me do some calculations while trying to keep the humor flowing.
First, let's convert 9600 milligrams to kilograms. Since there are 1000 milligrams in a gram, and 1000 grams in a kilogram, we divide 9600 by (1000 x 1000) to get 0.0096 kilograms.
Now, onto the cup dimension. Since fluid ounces and cups are related, with 1 cup being approximately 8 fluid ounces, we can perform a proportional conversion.
If 1 fluid ounce has a density of 9600 milligrams, then 8 fluid ounces (1 cup) will have a density of... well, 8 times that! So, we get 9600 x 8 milligrams.
Now, let's convert this back to kilograms. As before, we divide 9600 x 8 by (1000 x 1000) and voila, we get approximately 0.0768 kilograms per cup.
So, drumroll please... the density of that mysterious material is around 0.0768 kilograms per cup. Now, don't spill it, because ounces and cups can be quite fickle when it comes to fluids. Always keep an eye out for those sneaky conversions!
To convert the density from milligrams per fluid ounce to kilograms per cup, we need to perform a series of conversions. Here are the step-by-step calculations:
1. Convert 9600 milligrams to grams:
9600 milligrams = 9600 / 1000 = 9.6 grams
2. Convert grams to kilograms:
9.6 grams = 9.6 / 1000 = 0.0096 kilograms
3. Determine the volume of a cup:
The standard volume of a cup is 8 fluid ounces.
4. Convert 8 fluid ounces to milliliters:
8 fluid ounces ≈ 237 milliliters
5. Convert milliliters to liters:
237 milliliters = 237 / 1000 = 0.237 liters
6. Determine the density in kilograms per cup:
Density = (mass / volume)
Density = 0.0096 kilograms / 0.237 liters
Density ≈ 0.0405 kilograms per cup
Therefore, the density of the material is approximately 0.0405 kilograms per cup.
To express the density in kilograms per cup, we need to convert the given density from milligrams per fluid ounce to kilograms per cup.
First, let's convert 9600 milligrams to kilograms. Since there are 1000 milligrams in a gram and 1000 grams in a kilogram, we divide 9600 milligrams by 1000 to convert it to grams: 9600 mg ÷ 1000 = 9.6 grams.
Next, we convert grams to kilograms by dividing by 1000: 9.6 grams ÷ 1000 = 0.0096 kilograms.
Now, we need to determine the volume of a cup. The standard measurement for a cup is 236.588 milliliters (ml).
Since the given density is in milligrams per fluid ounce, we need to convert ml to fluid ounces. There are approximately 29.574 ml in one fluid ounce. So, 236.588 ml ÷ 29.574 = 8 fluid ounces.
Finally, we can express the density in kilograms per cup. We divide the mass in kilograms (0.0096 kg) by the volume in cups (8 cups): 0.0096 kg ÷ 8 cups ≈ 0.0012 kg/cup.
Therefore, the density of the material is approximately 0.0012 kilograms per cup.