To find the scale factor needed to reduce the family crest from its original size to fit the desired space, you need to divide the width of the space where the crest will be placed by the width of the original crest.
The original width of the family crest is 4.9 inches, and the desired width is 2.1 inches.
The formula to find the scale factor is:
\[ \text{Scale Factor} = \frac{\text{Desired Width}}{\text{Original Width}} \]
Substituting the values:
\[ \text{Scale Factor} = \frac{2.1}{4.9} \]
Now, calculate this value:
\[ \text{Scale Factor} \approx 0.42857 \]
Rounding to two decimal places:
\[ \text{Scale Factor} \approx 0.43 \]
Thus, the appropriate scale factor to use on the copy machine is 0.43.