A clinopyroxene crystal in a basalt, measured to have a composition of \( \text{Mg}_{1.2} \text{Fe}_{0.4} \text{Ca}_{0.4} \text{Si}_2 \text{O}_6 \), will have an Mg-number (Mg) of............%. (In integer)
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To calculate the Mg-number (Mg\#), divide the amount of Mg by the sum of Mg and Fe, then multiply by 100 to get the percentage.
Step 1: Define the Mg number.
The Mg number compares magnesium to the iron plus magnesium total, \[ \text{Mg\#} = \frac{\text{Mg}}{\text{Mg}+\text{Fe}}\times 100. \]
Step 2: Read the formula.
The pyroxene is $\text{Mg}_{1.2}\text{Fe}_{0.4}\text{Ca}_{0.4}\text{Si}_2\text{O}_6$. So Mg is 1.2 and Fe is 0.4.
Step 3: Add Mg and Fe.
Their sum is $1.2 + 0.4 = 1.6$.
Step 4: Work out the ratio.
So \[ \text{Mg\#} = \frac{1.2}{1.6}\times 100 = 75. \]
Step 5: State the answer.
The Mg number is 75 percent.
\[ \boxed{75} \]