Sure, let's solve these equations step by step.
### Step-by-Step Solution
We have a series of multiplication equations involving the number 63.85 and powers of 10. Our goal is to find the missing powers of 10 for each equation.
#### First Equation:
[tex]\[ 63.85 \times \square = 6,385 \][/tex]
To find the missing value, we can divide 6,385 by 63.85:
[tex]\[ \square = \frac{6,385}{63.85} = 100 \][/tex]
So, the missing power of 10 is 100.
#### Second Equation:
[tex]\[ 63.85 \times \square = 63,850 \][/tex]
Similarly, we divide 63,850 by 63.85:
[tex]\[ \square = \frac{63,850}{63.85} = 1,000 \][/tex]
Thus, the missing power of 10 is 1,000.
#### Third Equation:
[tex]\[ 63.85 \times \square = 638,500 \][/tex]
Again, we divide 638,500 by 63.85:
[tex]\[ \square = \frac{638,500}{63.85} = 10,000 \][/tex]
Therefore, the missing power of 10 is 10,000.
### Final Equations:
Putting the missing values back into the equations, we get:
[tex]\[
\begin{aligned}
63.85 \times 100 & = 6,385 \\
63.85 \times 1,000 & = 63,850 \\
63.85 \times 10,000 & = 638,500
\end{aligned}
\][/tex]
Thus, the complete equations with the determined powers of 10 are:
[tex]\[
\begin{aligned}
63.85 \times 100 & = 6,385 \\
63.85 \times 1,000 & = 63,850 \\
63.85 \times 10,000 & = 638,500
\end{aligned}
\][/tex]
