First, let's find the difference between the two numbers provided: 0.8 and 0.638.
Step 1: Subtract the smaller number from the larger number:
[tex]\[ 0.8 - 0.638 = 0.162 \][/tex]
Step 2: Now, we need to round this difference to the nearest tenth. The value 0.162 rounds to 0.2 when considering the tenths place. To round, we look at the hundredths place (the second digit after the decimal point) which is 6. Since 6 is greater than or equal to 5, we round up the tenths place.
Therefore, the rounded difference is:
[tex]\[ 0.2 \][/tex]
Thus, the closest choice to the estimated difference rounded to the nearest tenth is:
C) 0.2
