To determine what decimal value the digital scale should show when Daniel wants to buy [tex]\( 3 \frac{1}{5} \)[/tex] pounds of ham, let's convert the mixed fraction into a decimal value step-by-step.
1. Convert the mixed fraction to an improper fraction:
- First, recognize that [tex]\( 3 \frac{1}{5} \)[/tex] can be written as an addition of the whole number and the fraction:
[tex]\[
3 \frac{1}{5} = 3 + \frac{1}{5}
\][/tex]
- To convert it into an improper fraction, multiply the whole number part (3) by the denominator of the fraction (5) and add the numerator (1):
[tex]\[
3 \times 5 + 1 = 15 + 1 = 16
\][/tex]
- So, the improper fraction is:
[tex]\[
\frac{16}{5}
\][/tex]
2. Convert the improper fraction to a decimal:
- To convert [tex]\(\frac{16}{5}\)[/tex] to a decimal, perform the division of 16 by 5:
[tex]\[
\frac{16}{5} = 3.2
\][/tex]
Hence, the digital scale should show:
[tex]\[
\boxed{3.2}
\][/tex]
So, the scale should read [tex]\( 3.2 \)[/tex] pounds.
