Diamonds are measured in units called a carat. One carat equals 200mg. If a diamond is 0.600 carat, what is the mass of the diamond in ounces?
* 1kg=2.205 pounds* *1pound= 16 ounces* . . How do I get to the answer showing work/setting it up?
.6carat * 200mg/carat * 1kg/10^6mg * 2.205lb/kg * 16oz/lb = 0.00423 oz
To find the mass of the diamond in ounces, we need to convert the mass from carats to ounces.
First, we start by converting carats to grams. Since 1 carat is equal to 200mg, we can convert to grams using the following conversion factor: 1 carat = 0.2 grams (since 1 gram = 1000mg).
Now, we need to convert grams to kilograms. Since 1 kilogram is equal to 1000 grams, we divide the mass in grams by 1000 to convert to kilograms.
Next, we convert kilograms to pounds. Since 1 kilogram is equal to 2.205 pounds, we multiply the mass in kilograms by 2.205 to convert to pounds.
Finally, we convert pounds to ounces. Since 1 pound is equal to 16 ounces, we multiply the mass in pounds by 16 to convert to ounces.
Let's calculate step by step:
1 carat = 0.2 grams
0.600 carat = 0.600 * 0.2 grams = 0.120 grams
0.120 grams = 0.120 / 1000 kilograms (to convert to kilograms)
= 0.00012 kilograms
0.00012 kilograms = 0.00012 * 2.205 pounds (to convert to pounds)
= 0.0002646 pounds
0.0002646 pounds = 0.0002646 * 16 ounces (to convert to ounces)
= 0.0042336 ounces
So, the mass of the diamond is approximately 0.0042336 ounces.