QuestionA jeweler has 292 carats of diamonds. How many grams is that? (1 carat = $200 \mathrm{mg}$ )

Studdy Solution

STEP 1

Assumptions1. The mass of diamonds is292 carats.1 carat is exactly200 mg

STEP 2

We need to convert the mass of diamonds from carats to grams. We know that1 carat is exactly200 mg, and1 gram is exactly1000 mg. So, we can use these conversion factors to convert carats to grams.

STEP 3

First, we convert the mass of diamonds from carats to milligrams (mg) using the conversion factor1 carat =200 mg.
$Mass\, in\, mg = Mass\, in\, carats \\times Conversion\, factor\, (carats\, to\, mg)$

STEP 4

Now, plug in the given values for the mass in carats and the conversion factor to calculate the mass in mg.
$Mass\, in\, mg =292\, carats \\times200\, mg/carat$

STEP 5

Calculate the mass in mg.
$Mass\, in\, mg =292\, carats \\times200\, mg/carat =58400\, mg$

STEP 6

Next, we convert the mass from milligrams (mg) to grams (g) using the conversion factor1 g =1000 mg.
$Mass\, in\, g = Mass\, in\, mg / Conversion\, factor\, (mg\, to\, g)$

STEP 7

Plug in the values for the mass in mg and the conversion factor to calculate the mass in g.
$Mass\, in\, g =58400\, mg /1000\, mg/g$

STEP 8

Calculate the mass in g.
$Mass\, in\, g =58400\, mg /1000\, mg/g =58.4\, g$ The jeweler has58.4 grams of diamonds.

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